Abstract

CMOS image sensors with smaller pixels are expected to enable digital imaging systems with better resolution. When pixel size scales below 2 μm, however, diffraction affects the optical performance of the pixel and its microlens, in particular. We present a first-principles electromagnetic analysis of microlens behavior during the lateral scaling of CMOS image sensor pixels. We establish for a three-metal-layer pixel that diffraction prevents the microlens from acting as a focusing element when pixels become smaller than 1.4 μm. This severely degrades performance for on and off-axis pixels in red, green and blue color channels. We predict that one-metal-layer or backside-illuminated pixels are required to extend the functionality of microlenses beyond the 1.4 μm pixel node.

© 2010 OSA

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References

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  1. P. B. Catrysse and B. A. Wandell, “Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld,” Proc. SPIE 5678, 1–13 (2005).
    [CrossRef]
  2. H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzson, J. Ladd, I. Karasev, J. McKee, E. Jenkins, and W. Quinlin, “CMOS imager technology shrinks and image performance,” 2004 IEEE Workshop on Microelectronics and Electron. Devices, 7–18 (2004).
  3. K. B. Cho, C. Lee, S. Eikedal, A. Baum, J. Jiang, C. Xu, X. Fan, and R. Kauffman, “A 1/2.5 inch 8.1 Mpixel CMOS image sensor for digital cameras,” 2007 IEEE Intl. Solid-State Circuits Conf., 508–618 (2007).
  4. C. R. Moon, J. C. Shin, J. Kim, Y. K. Lee, Y. J. Cho, Y. Y. Yu, S. H. Hwang, B. J. Park, H. Y. Kim, S. H. Lee, J. Jung, S. H. Cho, K. Lee, K. Koh, D. Lee, and K. Kim, “Dedicated process architecture and the characteristics of 1.4 μm pixel CMOS image sensor with 8M density,” 2007 IEEE Symp. on VLSI Tech., 62–63 (2007).
  5. P. B. Catrysse and B. A. Wandell, “Optical efficiency of image sensor pixels,” J. Opt. Soc. Am. A 19(8), 1610–1620 (2002).
    [CrossRef]
  6. G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron. Dev. 50(1), 4–11 (2003).
    [CrossRef]
  7. J. Ahn, C. R. Moon, B. Kim, K. Lee, Y. Kim, M. Lim, W. Lee, H. Park, K. Moon, J. Yoo, Y. J. Lee, B. J. Park, S. Jung, J. Lee, T. H. Lee, Y. K. Lee, J. Jung, J. H. Kim, T. C. Kim, H. Cho, D. Lee, and Y. Lee, “Advanced image sensor technology for pixel scaling down toward 1.0μm,” 2008 IEEE Intl. Electron Dev. Meeting, 1–4 (2008).
  8. W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).
  9. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1985).
  10. D. M. Hartmann, O. Kibar, and S. C. Esener, “Characterization of a polymer microlens fabricated by use of the hydrophobic effect,” Opt. Lett. 25(13), 975–977 (2000).
    [CrossRef]
  11. K. Shinmou, K. Nakama, and T. Koyama, “Fabrication of micro-optic elements by the sol-gel method,” J. Sol-Gel Sci. Technol. 19(1/3), 267–269 (2000).
    [CrossRef]
  12. C. P. Lin, H. Yang, and C. K. Chao, “Hexagonal microlens array modeling and fabrication using a thermal reflow process,” J. Micromech. Microeng. 13(5), 775–781 (2003).
    [CrossRef]
  13. X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
    [CrossRef]
  14. A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech House, Boston, 2000).
  15. OptiFDTD, Optiwave Systems, Inc., http://www.optiwave.com
  16. J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
    [CrossRef]
  17. P. B. Catrysse and B. A. Wandell, “Integrated color pixels in 0.18-μm complementary metal oxide semiconductor technology,” J. Opt. Soc. Am. A 20(12), 2293–2306 (2003).
    [CrossRef]
  18. Y. Li, “Dependence of the focal shift on Fresnel number and f number,” J. Opt. Soc. Am. 72(6), 770 (1982).
    [CrossRef]
  19. C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Effects of imaging lens f-number on sub-2 μm CMOS image sensor pixel performance,” Proc. SPIE 7250, 72500G (2009).
    [CrossRef]
  20. S. Iwabuchi, Y. Maruyama, Y. Ohgishi, M. Muramatsu, N. Karasawa, and T. Hirayama, “A Back-illuminated high-sensitivity small-pixel color CMOS image sensor with flexible layout of metal wiring,” 2006 IEEE Intl. Solid-State Circuits Conf., 1171–1178 (2006).
  21. T. Joy, S. Pyo, S. Park, C. Choi, C. Palsule, H. Han, C. Feng, S. Lee, J. McKee, P. Altice, C. Hong, C. Boemler, J. Hynecek, M. Louie, J. Lee, D. Kim, H. Haddad, and B. Pain, “Development of a production-ready, back-illuminated CMOS image sensor with small pixels,” 2007 IEEE Intl. Electron Dev. Meeting, 1007–1010 (2007).
  22. C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Express 16(25), 20457–20470 (2008).
    [CrossRef] [PubMed]

2009 (1)

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Effects of imaging lens f-number on sub-2 μm CMOS image sensor pixel performance,” Proc. SPIE 7250, 72500G (2009).
[CrossRef]

2008 (1)

2005 (3)

P. B. Catrysse and B. A. Wandell, “Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld,” Proc. SPIE 5678, 1–13 (2005).
[CrossRef]

W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

2003 (3)

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron. Dev. 50(1), 4–11 (2003).
[CrossRef]

C. P. Lin, H. Yang, and C. K. Chao, “Hexagonal microlens array modeling and fabrication using a thermal reflow process,” J. Micromech. Microeng. 13(5), 775–781 (2003).
[CrossRef]

P. B. Catrysse and B. A. Wandell, “Integrated color pixels in 0.18-μm complementary metal oxide semiconductor technology,” J. Opt. Soc. Am. A 20(12), 2293–2306 (2003).
[CrossRef]

2002 (1)

2000 (2)

D. M. Hartmann, O. Kibar, and S. C. Esener, “Characterization of a polymer microlens fabricated by use of the hydrophobic effect,” Opt. Lett. 25(13), 975–977 (2000).
[CrossRef]

K. Shinmou, K. Nakama, and T. Koyama, “Fabrication of micro-optic elements by the sol-gel method,” J. Sol-Gel Sci. Technol. 19(1/3), 267–269 (2000).
[CrossRef]

1994 (1)

J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

1982 (1)

Agranov, G.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron. Dev. 50(1), 4–11 (2003).
[CrossRef]

Bérenger, J. P.

J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Berezin, V.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron. Dev. 50(1), 4–11 (2003).
[CrossRef]

Bu, J.

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

Catrysse, P. B.

Chao, C. K.

C. P. Lin, H. Yang, and C. K. Chao, “Hexagonal microlens array modeling and fabrication using a thermal reflow process,” J. Micromech. Microeng. 13(5), 775–781 (2003).
[CrossRef]

Cheong, W. C.

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

Esener, S. C.

Fesenmaier, C. C.

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Effects of imaging lens f-number on sub-2 μm CMOS image sensor pixel performance,” Proc. SPIE 7250, 72500G (2009).
[CrossRef]

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Express 16(25), 20457–20470 (2008).
[CrossRef] [PubMed]

Hartmann, D. M.

He, M.

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

Huo, Y.

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Effects of imaging lens f-number on sub-2 μm CMOS image sensor pixel performance,” Proc. SPIE 7250, 72500G (2009).
[CrossRef]

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Express 16(25), 20457–20470 (2008).
[CrossRef] [PubMed]

Hwang, S. B.

W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).

Kibar, O.

Kim, H. J.

W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).

Kim, J. S.

W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).

Kim, S. Y.

W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).

Koyama, T.

K. Shinmou, K. Nakama, and T. Koyama, “Fabrication of micro-optic elements by the sol-gel method,” J. Sol-Gel Sci. Technol. 19(1/3), 267–269 (2000).
[CrossRef]

Lee, J. G.

W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).

Lee, W. G.

W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).

Li, Y.

Lin, C. P.

C. P. Lin, H. Yang, and C. K. Chao, “Hexagonal microlens array modeling and fabrication using a thermal reflow process,” J. Micromech. Microeng. 13(5), 775–781 (2003).
[CrossRef]

Nakama, K.

K. Shinmou, K. Nakama, and T. Koyama, “Fabrication of micro-optic elements by the sol-gel method,” J. Sol-Gel Sci. Technol. 19(1/3), 267–269 (2000).
[CrossRef]

Niu, H. B.

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

Peng, X.

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

Shinmou, K.

K. Shinmou, K. Nakama, and T. Koyama, “Fabrication of micro-optic elements by the sol-gel method,” J. Sol-Gel Sci. Technol. 19(1/3), 267–269 (2000).
[CrossRef]

Tsai, R. H.

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron. Dev. 50(1), 4–11 (2003).
[CrossRef]

Wandell, B. A.

Yang, H.

C. P. Lin, H. Yang, and C. K. Chao, “Hexagonal microlens array modeling and fabrication using a thermal reflow process,” J. Micromech. Microeng. 13(5), 775–781 (2003).
[CrossRef]

Yu, W. X.

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

Yuan, X. C.

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

X. C. Yuan, W. X. Yu, M. He, J. Bu, W. C. Cheong, H. B. Niu, and X. Peng, “Soft-lithography-enabled fabrication of large numerical aperture refractive microlens array in hybrid SiO–TiO sol-gel glass,” Appl. Phys. Lett. 86(11), 114102 (2005).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

G. Agranov, V. Berezin, and R. H. Tsai, “Crosstalk and microlens study in a color CMOS image sensor,” IEEE Trans. Electron. Dev. 50(1), 4–11 (2003).
[CrossRef]

J. Comput. Phys. (1)

J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

J. Korean Phys. Soc. (1)

W. G. Lee, J. S. Kim, H. J. Kim, S. Y. Kim, S. B. Hwang, and J. G. Lee, “Two-dimensional optical simulation on a visible ray passing through inter-metal dielectric layers of CMOS image sensor device,” J. Korean Phys. Soc. 47, S434–S439 (2005).

J. Micromech. Microeng. (1)

C. P. Lin, H. Yang, and C. K. Chao, “Hexagonal microlens array modeling and fabrication using a thermal reflow process,” J. Micromech. Microeng. 13(5), 775–781 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Sol-Gel Sci. Technol. (1)

K. Shinmou, K. Nakama, and T. Koyama, “Fabrication of micro-optic elements by the sol-gel method,” J. Sol-Gel Sci. Technol. 19(1/3), 267–269 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (2)

P. B. Catrysse and B. A. Wandell, “Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld,” Proc. SPIE 5678, 1–13 (2005).
[CrossRef]

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Effects of imaging lens f-number on sub-2 μm CMOS image sensor pixel performance,” Proc. SPIE 7250, 72500G (2009).
[CrossRef]

Other (9)

S. Iwabuchi, Y. Maruyama, Y. Ohgishi, M. Muramatsu, N. Karasawa, and T. Hirayama, “A Back-illuminated high-sensitivity small-pixel color CMOS image sensor with flexible layout of metal wiring,” 2006 IEEE Intl. Solid-State Circuits Conf., 1171–1178 (2006).

T. Joy, S. Pyo, S. Park, C. Choi, C. Palsule, H. Han, C. Feng, S. Lee, J. McKee, P. Altice, C. Hong, C. Boemler, J. Hynecek, M. Louie, J. Lee, D. Kim, H. Haddad, and B. Pain, “Development of a production-ready, back-illuminated CMOS image sensor with small pixels,” 2007 IEEE Intl. Electron Dev. Meeting, 1007–1010 (2007).

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzson, J. Ladd, I. Karasev, J. McKee, E. Jenkins, and W. Quinlin, “CMOS imager technology shrinks and image performance,” 2004 IEEE Workshop on Microelectronics and Electron. Devices, 7–18 (2004).

K. B. Cho, C. Lee, S. Eikedal, A. Baum, J. Jiang, C. Xu, X. Fan, and R. Kauffman, “A 1/2.5 inch 8.1 Mpixel CMOS image sensor for digital cameras,” 2007 IEEE Intl. Solid-State Circuits Conf., 508–618 (2007).

C. R. Moon, J. C. Shin, J. Kim, Y. K. Lee, Y. J. Cho, Y. Y. Yu, S. H. Hwang, B. J. Park, H. Y. Kim, S. H. Lee, J. Jung, S. H. Cho, K. Lee, K. Koh, D. Lee, and K. Kim, “Dedicated process architecture and the characteristics of 1.4 μm pixel CMOS image sensor with 8M density,” 2007 IEEE Symp. on VLSI Tech., 62–63 (2007).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1985).

J. Ahn, C. R. Moon, B. Kim, K. Lee, Y. Kim, M. Lim, W. Lee, H. Park, K. Moon, J. Yoo, Y. J. Lee, B. J. Park, S. Jung, J. Lee, T. H. Lee, Y. K. Lee, J. Jung, J. H. Kim, T. C. Kim, H. Cho, D. Lee, and Y. Lee, “Advanced image sensor technology for pixel scaling down toward 1.0μm,” 2008 IEEE Intl. Electron Dev. Meeting, 1–4 (2008).

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech House, Boston, 2000).

OptiFDTD, Optiwave Systems, Inc., http://www.optiwave.com

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Figures (8)

Fig. 1
Fig. 1

(a) Two-dimensional (2D) pixel model with layer materials and thicknesses. (b) Electromagnetic calculation showing energy flow toward the photodiode (z-component of the Poynting vector Sz) with significant diffraction effects, reducing optical efficiency (transmission) and leading to spatial crosstalk even at normal incidence. The color scale in panel (b) is nonlinear to bring out detail in the regions of lower energy flow.

Fig. 2
Fig. 2

Poynting vector plots depicting energy flow toward the photodiode for (a) 1.75 μm, (b) 1.4 μm, and (c) 0.97 μm pixels for light with a 0° incidence angle and a wavelength of 650 nm. Only the center two pixels are shown and the boundaries between different materials are outlined. The color scale is nonlinear to bring out detail in the regions of lower energy flow.

Fig. 3
Fig. 3

Optimal microlens radius in a three-metal-layer pixel design for the 1.75, 1.4, 1.2, and 0.97 μm pixel nodes. Curves represent the optimized radii for the microlenses of pixels populating the red (solid line), green (dashed line) and blue (dotted line) color channels. The geometrical optics prediction, which depends on pixel height from microlens to photodiode only, is represented by the black dash-dot line.

Fig. 4
Fig. 4

Plots of (a) normalized optical efficiency (OE) and (b) normalized optical crosstalk (OX) in a three-metal-layer pixel design for the 1.75, 1.4, 1.2, and 0.97 μm pixel nodes. Curves represent normalized OE and OX for pixels in the red, green and blue color channels.

Fig. 5
Fig. 5

Poynting vector plots depicting energy flow toward the photodiode for (a) 1.75 μm, (b) 1.4 μm, and (c) 0.97 μm pixels for 650-nm light at oblique incidence with a 30° incidence angle. Only the center pixels are shown and the boundaries between different materials are outlined.

Fig. 6
Fig. 6

Comparison of on- (0-deg) and off-axis (30-deg) optical performance. Plots of (a) normalized optical efficiency (OE) and (b) normalized optical crosstalk (OX) in a three-metal-layer pixel design for several pixel nodes below 2 μm. The solid black curve and dashed blue curves represent the normalized OE (panel a) and OX (panel b) for the on-axis and off-axis, respectively.

Fig. 7
Fig. 7

Poynting vector plots depicting energy flow toward the photodiode for a 0.97 μm (a) three-metal-layer, (b) two-metal-layer and (c) one-metal-layer pixel subject to light with a 0° incidence angle and a wavelength of 650 nm.

Fig. 8
Fig. 8

Plots of (a) normalized optical efficiency (OE) and (b) normalized optical crosstalk (OX) versus pixel stack height for different pixel sizes. The stack heights of 4.04 μm, 3.46 μm and 2.74 μm represent three-, two- and one-metal-layer pixels, respectively. Solid black, dashed red, and dotted blue curves represent the normalized OE (panel a) and OX (panel b) for 1.4, 1.2, and 0.97-μm pixel designs.

Equations (1)

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r = f ( n M L n a i r ) n eff

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