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The shrinkage of pixel size down to sub-2 μm in high-resolution CMOS image sensors (CISs) results in degraded efficiency and increased crosstalk. The backside illumination technology can increase the efficiency, but the crosstalk still remains an critical issue to improve the image quality of the CIS devices. In this paper, by adopting a parabolic color filter (P-CF), we demonstrate efficiency enhancement without any noticeable change in optical crosstalk of a backside illuminated 1.12 μm pixel CIS with deep-trench-isolation structure. To identify the observed results, we have investigated the effect of radius of curvature (r) of the P-CF on the efficiency and optical crosstalk of the CIS by performing an electromagnetic analysis. As the r of P-CF becomes equal to (or half) that of the microlens, the efficiencies of the B-, G-, and R-pixels increase by a factor of 14.1% (20.3%), 9.8% (15.3%), and 15.0% (15.7%) with respect to the flat CF cases without any noticeable crosstalk change. Also, as the incident angle increases up to 30°, the angular dependence of the efficiency and crosstalk significantly decreases by utilizing the P-CF in the CIS. Meanwhile, further reduction of r severely increases the optical crosstalk due to the increased diffraction effect, which has been confirmed with the simulated electric-field intensity distribution inside the devices.
© 2016 Optical Society of America
1. Introduction
Complementary metal oxide silicon (CMOS) image sensors have been widely adopted in mobile devices, due to various advantages such as low voltage operation, low power consumption, compatibility with standard CMOS technology, and integration capability. Over the past decade, significant improvements in the performance of CMOS image sensors (CISs) have been achieved with the down-scaling of the feature sizes in CMOS technology [1, 2]. However, decreasing the pixel size of CIS devices to the sub-2-μm range degrades quantum efficiency (QE), as well as increases optical and electrical crosstalks [3–6]. Thus, backside illumination technology has been utilized to increase the QE because it eliminates the need of metal layers between microlens (ML) and photodiodes with reducing the optical loss [7–9]. Meanwhile, the deep-trench-isolation (DTI) structure, which is filled with lower refractive index materials compared to Si photodiodes, has proven to be effective in blocking the electrical crosstalk in the deep quasi-neutral region as well as the optical crosstalk through the active Si layer [10–12].
The pixel spectral response of CIS devices depends on the optical property of color filter (CF) materials, final pattern thickness of CF layer, and optical stack height. The spectral crosstalk is related to the optical transmittance of the CFs in a range of wavelengths where they have to be opaque. The optical crosstalk is induced by photon penetration to neighboring pixels before electron/hole pair generation, which mainly occurs in the region between the ML and the photodiodes due to reflection, refraction or diffraction effects [13]. Thus, the methods employing lens-shaped CF layers have been suggested to increase the effective CF thickness and decrease the optical stack [14,15]. However, as the pixel size approaches the wavelength of visible light, optical crosstalk is still induced by diffraction effect in the stacked layers on the top of Si-photodiodes. Moreover, there have been no quantitative studies of the effect of modified CF shapes on the efficiency and optical crosstalk of a backside illuminated CIS with the DTI structure. Therefore, in this paper, we systematically performed an electromagnetic analysis of parabolic color filters (P-CFs) with a different radius of curvature (r) with the size equal to or smaller than that of ML, by integrating them in a backside illuminated 1.12 μm pixel CIS with the DTI structure. The Finite-Difference Time-Domain (FDTD) method [16] was utilized to investigate the effect of r of the suggested P-CF structure on the efficiency and optical crosstalk of the CIS device at both normal (0°) and oblique incidence up to 30°. The results show that as the r of P-CF is reduced from the size of ML to half the size of it, the efficiency monotonously increases without any noticeable change in the optical crosstalk with respect to the flat CF case, while further reduction of r severely increases the spatial optical crosstalk due to the diffraction effect. Also, the simulated electric-field intensity distributions inside the devices confirm that the P-CF with r equal to or half that of ML makes the incident light more concentrated towards the photodiodes, while further reduction in r causes significant increase in lateral light leakage, leading to increased optical crosstalk.
2. Device Structure and calculation method
Figure 1 shows the schematics of typical pixel structures of a backside illuminated CIS, consisting of a Si substrate with photodiodes separated by the DTI layer, SiNx anti-reflection layer, flat CF or P-CF, and ML array. Here, the CF layers are constructed with a conventional 4 pixel unit with Bayer array configuration; two green (G), one blue (B), and one red (R) filters [17]. Three dimensional (3D) views of the adjacent flat G- and B-pixels and the adjacent flat G- and R-pixles are represented in Figs. 1(a) and 1(c), respectively. The cross-sectional views in the x-z plane of the P-CF (conic constant of −1) pixels with different r values of 1 μm, 0.5 μm, and 0.25 μm are shown in Figs. 1(b) and 1(d) in comparison with the flat CF case. To investigate the efficiency and optical crosstalk between the adjacent color pixels, the performance of the CISs adopting the P-CFs was compared with that of the deviceemploying the flat CF layer. Here, we selected some typical values of the layered structures because the thickness and position of each layer in commercial CISs can vary depending on the specific fabrication process. The ML with r of 1 μm was made of a high-refractive-index polymer (n~1.6) with a thickness of 360 nm, and the P-CF layers with different values of r were constructed with a thickness of 600 nm at the center. The SiNx with a thickness of 100 nm as an antireflection layer was adopted, and the DTI layer surrounding the Si-photodiodes was constructed with 2.5-μm-height SiO2 material (n~1.5). Table 1 summarizes the complex refractive indices of materials adopted in this study. The Si (n~4) photodiode underlying each CF layer was selected to have an area of 1.12 × 1.12 μm2 because CF patterning in the sub-μm size is limited by current photo-lithography process.
Fig. 1 Schematics of a backside illuminated 1.12 μm pixel CMOS image sensor with DTI structure. The 3D views of (a) the flat G- and B-pixels and (b) their cross-section view in x-z plane compared to those of the pixels with P-CFs with r of 1 μm (R = 1), 0.5 μm (R = 0.25), and 0.25 μm (R = 0.25). The 3D views of (b) the flat G- and R-pixels and (d) their cross-section view in comparison with those of the pixels with P-CFs.
Table 1. Real (n) and imaginary (k) parts of the complex refractive indices of the materials.
To analyze the dependence of the efficiency and the spatial optical crosstalk of adjacent color pixels on the r of P-CFs and the incidence angle of lightwave, we performed full electromagnetic wave simulation using a 3D-FDTD simulation package (Expert CIS, Daou Incube Ltd.) [18]. Here, Si-photodiode separated by the DTI structure, SiNx, CF, and ML were placed from the bottom to the top along the + z-direction and extended along the x-y plane. A perfectly matched absorbing boundary layer was used at bottom edge to prevent reflections along the z-direction, and a periodical boundary condition at left and right edges was applied to limit simulation time and to discount boundary layer effects along the x- and y- directions. The simulation grid size was set to 10 nm as a minimum element position increment. In order to simulate these multilayer structures properly, a modified Drude-Lorentz model [19,20] was used to describe the permittivity of dispersive materials as below
where ε∞, ωp, ωop, γp, and γp' are the relative permittivity at infinite frequency, the plasma frequency, the resonance frequency, the damping factor, and the fitting parameter, respectively. Then, the measured complex refractive indices of ML, CF layer, Si, and SiO2 were fitted by a rational fraction approach [21] combined with multi-pole fitting algorithm [22] to extract complex multi-poles corresponding to the modified Drude–Lorentz dispersive model in the time-domain simulation. The incident light was modeled as a continuous plane wave excitation in air just above the microlens surface with a wavelength from 400 nm to 700 nm along the z-axis at a backward direction towards the adjacent G- and B-pixels or G- and R-pixels. Then, the efficiencies of the sensor pixels were estimated as the ratio of the transmitted optical power through the CF-layer on the surface of Si photodiodes to the incident optical power.3. Results and discussion
A properly designed ML focuses an incident light into the Si-photodiode through the CF layer to reduce unwanted scattering and crosstalk. The CF layers we used in this study transmit the light in the wavelength range of 400 nm to 480 nm for B-pixel, 490 nm to 610 nm for G-pixel, and 620 nm to 700 nm for R-pixel. Accordingly, the efficiencies of the color pixels in the CIS devices are observed in those wavelength ranges. Figures 2(a)-2(c) show the efficiencies of the pixels with different shapes of CF layers in the visible wavelength range of 400 nm to 700 nm under different incidence angles of 0°, 15°, and 30°, respectively. The estimated efficiencies of the pixels with the P-CFs are higher than that of the flat CF case for the normal and oblique incidence angles. As the r of P-CF decreases from 1 μm to 0.25 μm, the efficiencies of the color pixels increase, while these efficiencies gradually decrease with increasing the incident angle. Here, the efficiencies of R-pixel are lower than those of B- or G-pixels because the extinction coefficient (k) at a high-tranmission spectral range for the R-CF layer is relatively higher than that for the B- or G-CF layer as shown in Table 1.
Fig. 2 Plots of optical efficiency of the pixels employing the P-CF with r of 1 μm (R = 1), 0.5 μm (R = 0.5), 0.25 μm (R = 0.25) in comparison with the flat CF case for a light with an incidence angle of (a) 0°, (b) 15°, and (c) 30°. Here, CF_GB (or CF_GR) represents the efficiency of the adjacent G- and B –pixel (or the adjacent G- and R-pixel).
To quantify the dependence of the efficiency and optical crosstalk on the r of P-CF and the incidence angle, we simulated the variation of the peak efficiency and spatial optical crosstalk as shown in Figs. 3(a) and 3(b), respectively. For the normal incidence case, the peak efficiencies of the sensor pixels underlying the flat B-, G-, and R-CF are estimated to be 56.1%, 53.9%, and 38.9%, respectively. As the r of the P-CF layer coincides with that (r = 1 μm) of the ML, the peak efficiencies of the pixels underlying the parabolic B-, G-, and R-CF become 62.9%, 58.2%, and 43.1%, respectively. Thus, the efficiencies of the pixels with the parabolic B-, G-, and R-CFs increase by a factor of 12.1%, 8.0%, and 10.8% with respect to those with the flat CFs. As r decreases to 0.5 μm (0.25 μm), the peak efficiencies of the pixels with parabolic B-, G-, and R-CFs become 66.6% (70.7%), 60.6% (71.7%), and 43.7% (49.6%), respectively, which corresponds to the efficiency increase by a factor of 18.7% (26.0%), 12.4% (33.0%), and 12.3% (27.5%) with respect to the flat CF cases. Even for the oblique incident angles, the observed efficiencies of the pixels adopting the P-CFs show higher values than the flat CF cases as shown in Fig. 3(a). Also, the efficiency of the CIS device with the P-CF degrades much less than that of the flat CF case when the incident angle of light increases from 0° to 30°. That is, the efficiencies of the pixels adopting the parabolic B-, G-, and R-CF with the r of 1 μm (0.5 μm) at the incidence angle of 30° decrease by a factor of 14.0% (13.1%), 9.3% (7.9%), and 17.2% (17.9%), respectively, with respect to 0° incidence angle case, which are much smaller than the flat CF cases (19.1% for B-pixel, 12.1% for G-pixel, and 25.7% for R-pixel).
Fig. 3 Plots of (a) efficiency variation and (b) crosstalk change as a function of the incidence angle for each B-, G-, and R–pixel adopting the P-CF with different values of r such as 1 μm (R = 1), 0.5 μm (R = 0.5), and 0.25 μm (R = 0.25), in comparison with the pixel with the flat CF.
Meanwhile, the tails of the efficiency curves in Fig. 2 indicate the magnitude of spatial optical crosstalk. The optical crosstalk in each pixel with the B-CF was estimated as the ratio of average efficiency in the wavelength of 490 nm to 700 nm (transmission region of G- and R-CFs) to the average efficiency in 400 nm to 480 nm (transmission region of B-CF). The crosstalks for the sensor pixels underlying the G- and R-CFs were evaluated with the same procedure, as shown in Fig. 3(b) for the sensor pixels with different shapes of CF layers. It is observed that as r decreases from 1 μm to 0.5 μm, the optical crosstalk of the pixel employing the P-CF with r of 1 μm or 0.5 μm slighly increases compared to the flat CF cases at incidence angles of 0° and 15°, while the difference in the optical crosstalk between the two cases decreases for higher incidence angle of 30° due to the parabolic shape of the CF. Meanwhile, as r is further reduced to 0.25 μm, significant increase in optical crosstalk is observed, implying degradation of image quality. This increased optical crosstalk can be attributed to the increased light scattering and diffraction by the P-CF with a redued thickness near the DTI layer.
To investigate the overall performance of the CISs with different CF shapes in terms of efficiency and optical crosstalk, the average values of efficiency and optical crosstalk over incidence angles were calculated as shown in Fig. 4. As seen in the Figs. 2 and 3, the pixels with the P-CF show higher efficiencies than the flat CF cases. The average efficiencies of the pixels with parabolic B-, G-, and R-CFs with r of 1 μm (0.5 μm) increase by a factor of 14.1% (20.3%), 9.8% (15.3%), and 13.2% (15.7%) with respect to the one with the flat CF, while the optical crosstalk doesn’t show any noticeable change for the P-CF with r of 1 μm and 0.5 μm. For the case of the P-CF with r of 0.25 μm, the optical crosstalk significntly increases, even though the efficiencies of the pixels employing the parabolic B-, G-, and R-CFs with r of 0.25 μm highly increase by a factor of 27.5%, 34.4%, and 28.8% with respect to the flat CF case. The observed results can be explained by noting that the reduced thickness of the CF layers increases the spectral crosstalk, and the curved shape of the CF increases the spatial optical crosstalk due to the diffraction effect. Therefore, it can be concluded that the pixels underlying the parabolic B-, G-, and R-CFs with the r equal to or half that of the ML inceases in efficiency without any appreciable crosstalk change, compared to the case with flat CF layers. These enhancements will effectively increase the signal-to-noise ratio of the pixels, consequenty improving the image quality of sub 2-μm pixel CIS devices. Meanwhile, the device adopting the P-CF with the r less than half that of ML causes a significant increase in optical crosstalk even though there is a high increase in the efficiency.
Fig. 4 Plots of (a) average efficiency and (b) crosstalk change over incidence angles depending on different shapes of the CFs: Flat CF, P-CF with r of 1 μm (R = 1), 0.5 μm (R = 0.5), and 0.25 μm (R = 0.25).
To elucidate the light diffraction effect in the region between the ML and the Si-photodiodes with different CF shapes, the electric-field profiles inside the sensor pixels were analyzed by varying the incidence angle. Figures 5 and 6 show the simulated electric-field distributions of adjacent G- and B-pixels, and adjacent G- and R-pixels, respectively, in the x-z plane for a light at a wavelength of 550 nm. It is observed that the DTI layer guides well the incident light into the Si photodiode for all the cases, due to the total internal reflection at the boundary between the Si bulk with a high refractive index and the SiO2 with a low refractive index. Also, we can observe that the diffraction from the top surface of P-CF is relatively smaller than that from the flat CF, and the parabolic shape of P-CF makes the incident light more concentrated towards the Si photodiodes at both normal and oblique incidence angles. When we compare the distribution of electric-field intensity for the three different P-CF structures, it is observed that the area of high electric-field intensity in the photodiode of G-pixel increases as the r of the P-CF decreases. Meanwhile, there are noticeable increases in the electric-field intensity in the adjacent B- or R-pixels adopting the P-CF with r of 0.25 μm. These results confirm the efficiency increase with decreasing r of the P-CF and the significant increase in optical crosstalk for the devices employing the P-CF with r of 0.25 μm as demonstrated in Figs. 3 and 4. For the adjacent B- or R-pixels at oblique incidence angles, it is observed that the electric-field intensities in the photodiode underlying the P-CF with r of 1 μm or 0.5 μm have levels similar to the case of flat CFs. Meanwhile, a noticeable increase inelectric-field intensity inside the DTI layer can be seen at high oblique angles for the devices adopting the P-CF with r of 0.25 μm. This shows that the unfiltered light from the thin CF layer propagates through the DTI layer, leading to the increased optical crosstalk as demonstrated in Figs. 3 and 4. Therefore, by adjusting the r of the suggested P-CF layer, we can optimize the structure of a sub-μm pixel CIS device to significantly improve the efficiency without any optical crosstalk increase taking into account the performances under normal and oblique illumination.
Fig. 5 Cross-sectional |E|2 field distribution normalized to the incident field for the G-and B-pixels with the flat CF or the P-CFs with different values of r such as 1 μm (R = 1), 0.5 μm (R = 0.5), and 0.25 μm (R = 0.25) by varying the incidence angle from (a) 0°, (b) 15°, and (c) 30°. The field distributions were calculated for a light with a wavelength of 550 nm.
Fig. 6 Cross-sectional |E|2 field distribution normalized to the incident field for the G-and R-pixels with the flat CF or the P-CFs with different values of r such as 1 μm (R = 1), 0.5 μm (R = 0.5), and 0.25 μm (R = 0.25) by varying the incidence angle from (a) 0°, (b) 15°, and (c) 30°. The field distributions were calculatedfor a light with a wavelength of 550 nm.
4. Conclusion
The effect of P-CFs on the efficiency and optical crosstalk of a backside illuminated 1.12 μm pixel CIS device with the DTI structure was investigated by varying the radius of curvature (r) of the P-CF and the angle of incident light. When the r of the P-CF coincides with that of the ML, the average efficiencies increase by a factor of 14.1%, 9.8%, and 15%, respectively, compared to the flat CF case, for all the incidence angles of the sensor pixels underlying the parabolic B-, G-, and R-CFs. As r decreases to half that of ML, the average efficiencies are further improved by a factor of 20.3%, 15.3%, and 15.7% for B-, G, and R-pixels, respectively. As the r of P-CF becomes less than half that of ML, the optical crosstalk between the adjacent pixels also increases noticeably due to the increased light scattering and diffraction effects from the optical stack including the P-CF. The simulated electric-field intensity distributions inside each Si photodiode verify that the P-CF with r equal to or half that of ML makes the incident light more concentrated towards photodiodes, while further reduction in r causes lateral light leakage to the adjacent pixels, leading to the degradation of image quality. Our results will serve as a guide towards increase of the signal-to-noise ratio of the pixels, consequently improving the image quality of sub 2-μm pixel CIS devices.
Acknowledgments
This research was supported by the National Research Foundation (NRF) funded by the Korea Ministry of Science, ICT, and Future Planning (No: 2015R1A2A2A04002733).
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