Abstract

This paper describes a new methodology we have developed for the optical simulation of CMOS image sensors. Finite Difference Time Domain (FDTD) software is used to simulate light propagation and diffraction effects throughout the stack of dielectrics layers. With the use of an incoherent summation of plane wave sources and Bloch Periodic Boundary Conditions, this new methodology allows not only the rigorous simulation of a diffuse-like source which reproduces real conditions, but also an important gain of simulation efficiency for 2D or 3D electromagnetic simulations. This paper presents a theoretical demonstration of the methodology as well as simulation results with FDTD software from Lumerical Solutions.

© 2007 Optical Society of America

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References

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  1. A. El Gamal and H. Eltoukhy, “CMOS Image Sensors. An introduction to the technology, design, and performance limits, presenting recent developments and future directions,” IEEE Circuits & Devices Magazine(May/June 2005).
  2. E. R. Fossum, “CMOS Image Sensors: Electronic Camera-On-A-Chip,” IEEE Trans. Electron. Devices 44, 1689–1698 (1997).
    [Crossref]
  3. P. B. Catrysse, X. Liu, and A. El Gamal, “QE Reduction due to Pixel Vignetting in CMOS Image Sensors”, Proc. SPIE 3965, 420–430 (2000).
    [Crossref]
  4. P. B. Catrysse and B. A. Wandell, “Optical efficiency of image sensor pixels,” J. Opt. Soc. Am A 19, 1610–1620 (2002).
    [Crossref]
  5. J. Vaillant and F. Hirigoyen, “Optical simulation for CMOS imager microlens optimization,” Proc. SPIE 5459, 200–210 (2004).
    [Crossref]
  6. H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).
  7. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [Crossref]
  8. A. Taflove and S. C. Hagness, Computational Electrodynamics : the finite-difference time-domain method, 2nd Edition, H. E. Schrank, Series Editor (Artech House, Boston, Ma, 2000).
  9. Lumerical Solutions, Inc. http://www.lumerical.com.
  10. J. W. Goodman, Introduction to Fourier Optics, 3rd Edition (Roberts & Company Publishers, Englewood, Co, 2005), Chap. 5.
    [PubMed]

2005 (1)

A. El Gamal and H. Eltoukhy, “CMOS Image Sensors. An introduction to the technology, design, and performance limits, presenting recent developments and future directions,” IEEE Circuits & Devices Magazine(May/June 2005).

2004 (2)

J. Vaillant and F. Hirigoyen, “Optical simulation for CMOS imager microlens optimization,” Proc. SPIE 5459, 200–210 (2004).
[Crossref]

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

2002 (1)

P. B. Catrysse and B. A. Wandell, “Optical efficiency of image sensor pixels,” J. Opt. Soc. Am A 19, 1610–1620 (2002).
[Crossref]

2000 (1)

P. B. Catrysse, X. Liu, and A. El Gamal, “QE Reduction due to Pixel Vignetting in CMOS Image Sensors”, Proc. SPIE 3965, 420–430 (2000).
[Crossref]

1997 (1)

E. R. Fossum, “CMOS Image Sensors: Electronic Camera-On-A-Chip,” IEEE Trans. Electron. Devices 44, 1689–1698 (1997).
[Crossref]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

Agranov, G.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Boettiger, U.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Bruce, J.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Catrysse, P. B.

P. B. Catrysse and B. A. Wandell, “Optical efficiency of image sensor pixels,” J. Opt. Soc. Am A 19, 1610–1620 (2002).
[Crossref]

P. B. Catrysse, X. Liu, and A. El Gamal, “QE Reduction due to Pixel Vignetting in CMOS Image Sensors”, Proc. SPIE 3965, 420–430 (2000).
[Crossref]

Eltoukhy, H.

A. El Gamal and H. Eltoukhy, “CMOS Image Sensors. An introduction to the technology, design, and performance limits, presenting recent developments and future directions,” IEEE Circuits & Devices Magazine(May/June 2005).

Fan, X.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Fossum, E. R.

E. R. Fossum, “CMOS Image Sensors: Electronic Camera-On-A-Chip,” IEEE Trans. Electron. Devices 44, 1689–1698 (1997).
[Crossref]

Gamal, A. El

A. El Gamal and H. Eltoukhy, “CMOS Image Sensors. An introduction to the technology, design, and performance limits, presenting recent developments and future directions,” IEEE Circuits & Devices Magazine(May/June 2005).

P. B. Catrysse, X. Liu, and A. El Gamal, “QE Reduction due to Pixel Vignetting in CMOS Image Sensors”, Proc. SPIE 3965, 420–430 (2000).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd Edition (Roberts & Company Publishers, Englewood, Co, 2005), Chap. 5.
[PubMed]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics : the finite-difference time-domain method, 2nd Edition, H. E. Schrank, Series Editor (Artech House, Boston, Ma, 2000).

Hirigoyen, F.

J. Vaillant and F. Hirigoyen, “Optical simulation for CMOS imager microlens optimization,” Proc. SPIE 5459, 200–210 (2004).
[Crossref]

Hong, C.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Jenkins, E.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Karasev, I.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Ladd, J.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Li, J.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Liu, X.

P. B. Catrysse, X. Liu, and A. El Gamal, “QE Reduction due to Pixel Vignetting in CMOS Image Sensors”, Proc. SPIE 3965, 420–430 (2000).
[Crossref]

Mauritzon, R.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

McKee, J.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Mouli, C.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Panicacci, R.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Patrick, I.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Quinlin, W.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Rhodes, H.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Smith, S.

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics : the finite-difference time-domain method, 2nd Edition, H. E. Schrank, Series Editor (Artech House, Boston, Ma, 2000).

Vaillant, J.

J. Vaillant and F. Hirigoyen, “Optical simulation for CMOS imager microlens optimization,” Proc. SPIE 5459, 200–210 (2004).
[Crossref]

Wandell, B. A.

P. B. Catrysse and B. A. Wandell, “Optical efficiency of image sensor pixels,” J. Opt. Soc. Am A 19, 1610–1620 (2002).
[Crossref]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

IEEE (1)

H. Rhodes, G. Agranov, C. Hong, U. Boettiger, R. Mauritzon, J. Ladd, I. Karasev, J. McKee, E. Jenkins, W. Quinlin, I. Patrick, J. Li, X. Fan, R. Panicacci, S. Smith, C. Mouli, and J. Bruce, “CMOS Imager Technology Shrinks and Image Performance,” IEEE (2004).

IEEE Circuits & Devices Magazine (1)

A. El Gamal and H. Eltoukhy, “CMOS Image Sensors. An introduction to the technology, design, and performance limits, presenting recent developments and future directions,” IEEE Circuits & Devices Magazine(May/June 2005).

IEEE Trans. Antennas Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

IEEE Trans. Electron. Devices (1)

E. R. Fossum, “CMOS Image Sensors: Electronic Camera-On-A-Chip,” IEEE Trans. Electron. Devices 44, 1689–1698 (1997).
[Crossref]

J. Opt. Soc. Am A (1)

P. B. Catrysse and B. A. Wandell, “Optical efficiency of image sensor pixels,” J. Opt. Soc. Am A 19, 1610–1620 (2002).
[Crossref]

Proc. SPIE (2)

J. Vaillant and F. Hirigoyen, “Optical simulation for CMOS imager microlens optimization,” Proc. SPIE 5459, 200–210 (2004).
[Crossref]

P. B. Catrysse, X. Liu, and A. El Gamal, “QE Reduction due to Pixel Vignetting in CMOS Image Sensors”, Proc. SPIE 3965, 420–430 (2000).
[Crossref]

Other (3)

A. Taflove and S. C. Hagness, Computational Electrodynamics : the finite-difference time-domain method, 2nd Edition, H. E. Schrank, Series Editor (Artech House, Boston, Ma, 2000).

Lumerical Solutions, Inc. http://www.lumerical.com.

J. W. Goodman, Introduction to Fourier Optics, 3rd Edition (Roberts & Company Publishers, Englewood, Co, 2005), Chap. 5.
[PubMed]

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Figures (9)

Fig. 1.
Fig. 1.

CMOS image sensor: schematic (left) and SEM picture (center) of CMOS pixel, and the final module (right).

Fig. 2.
Fig. 2.

Light shape in case of a uniform pixel illumination provided by an objective lens.

Fig. 3.
Fig. 3.

Schematic representation of the light source.

Fig. 4.
Fig. 4.

The “thin lens” source simulated by the FDTD software from Lumerical.

Fig. 5.
Fig. 5.

Layout of the simulated structure (left) and intensity in the focal plane for different number of Gaussian waves (right).

Fig. 6.
Fig. 6.

Schematic of the light source with the different parameters

Fig. 7.
Fig. 7.

Poynting results of the simulated structure for on-axis pixels: propagation along the structure (top) and results at Silicon interface, y=0μm (bottom). On the left the 5 pixels with the Gaussian sources (“thin lens”). On the right, the 5 pixels with 16 plane wave sources (top) and different numbers of plane waves (bottom).

Fig. 8.
Fig. 8.

Poynting results of the simulated structure for off-axis pixels (10° shift): propagation along the structure (top) and results at Silicon interface, y=0μm (bottom). On the left the 5 pixels with the Gaussian sources (“thin lens”). On the right, the 5 pixels with 16 plane wave sources (top) and different numbers of plane waves (bottom).

Fig. 9.
Fig. 9.

Comparison of the 2 methods: Poynting vector at Silicon interface for the central pixel For on-axis pixels (on the left) and off-axis pixels with 10° shift (on the right)

Tables (1)

Tables Icon

Table 1. Comparison of the two methodologies for 3D simulation. In both cases, two polarization states must be simulated to calculate the response to unpolarized light. The Bloch boundary conditions used for the second solution require complex-valued fields

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

I x 0 , y 0 ( x f , y f ) = A 2 λ 2 f 2 t ( x , y ) e 2 λf [ x ( x f + x 0 ) + y ( y f + y 0 ) ] dxdy 2
I f = I x 0 , y 0 ( x f , y f ) d x 0 d y 0
I f = A 2 t ( x , y ) e 2 λf ( x . x f + y . y f ) e 2 λf ( x . x 0 + y . y 0 ) dxdy 2 d ( x 0 λf ) d ( y 0 λf )
I f = A 2 FT { t ( x , y ) e 2 λf ( x . x f + y . y f ) } ( x 0 λf , y 0 λf ) 2 d ( x 0 λf ) d ( y 0 λf )
FT { f ( x , y ) } ( u , v ) 2 dudv = f ( x , y ) 2 dxdy
I f = A 2 t ( x , y ) e 2 λf ( x . x f + y . y f ) 2 dxdy
I f = A 2 t ( x , y ) 2 dxdy
k = k x x + k y y = 2 π λ α x + 2 π λ β y
I f = A 2 ( λf 2 π ) 2 t ( λf 2 π k x , λf 2 π k y ) 2 d k x d k y
t ( k x , k y ) = P ( k x , k y ) = { 1 , k x 2 + k y 2 N A * k 2 0 , else
I PW = A e i ( k x x + k y y ) . W ( k x , k y ) 2 d k x d k y
I PW = A 2 W ( k x , k y ) 2 d k x d k y
T = a 2 a 2 1 2 P y ( x ) dx

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