Abstract

We report on the modulation transfer function (MTF) in short-wave infrared indium gallium arsenide (InGaAs) on indium phosphide (InP) planar photodetector arrays. Our two-dimensional numerical method consists of optical simulations using the finite-difference time domain method and drift-diffusion simulations using the finite-element method. This parametric study investigates MTF dependence on pitch, the addition of refractive microlenses, the thickness of the InGaAs absorber, and the doping concentration of the InGaAs absorber. A focus is placed on the connection between the lateral diffusion of photogenerated holes in InGaAs and the MTF. It is found that the MTF of small-pitch arrays exhibit sub-ideal behavior due to pixel cross-talk resulting from a long minority carrier diffusion length. By incorporating monolithic microlenses with the InP substrate, the MTF response is improved for all pitches investigated, particularly for spatial frequencies near the respective cutoff frequencies. We also find a strong dependence of the MTF on the thickness and doping concentration in the absorbing region. Trends in dark current and quantum efficiency are reported.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. G. C. Holst, “Imaging system performance based upon Fλ/d,” Opt. Eng. 46(10), 103204 (2007).
    [Crossref]
  2. G. C. Holst and R. G. Driggers, “Small detectors in infrared system design,” Opt. Eng. 51(9), 096401 (2012).
    [Crossref]
  3. R. G. Driggers, R. H. Vollmerhausen, J. P. Reynolds, J. D. Fanning, and G. C. Holst, “Infrared detector size: how low should you go?” Opt. Eng. 51(6), 063202 (2012).
    [Crossref]
  4. H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
    [Crossref]
  5. A. R. Wichman, R. E. DeWames, and E. Bellotti, “Three-dimensional numerical simulation of planar P+n heterojunction In0.53Ga0.47As photodiodes in dense arrays part I: dark current dependence on device geometry,” Proc. SPIE 9070, 907003 (2014).
    [Crossref]
  6. M. Gallant and A. Zemel, “Long minority hole diffusion length and evidence for bulk radiative recombination limited lifetime in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 52, 1686 (1988).
    [Crossref]
  7. A. Zemel, U. Mizrahi, and T. Fishman, “Nondestructive measurement of the minority carrier diffusion length in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 101, 133501 (2012).
    [Crossref]
  8. H. Zappe, Fundamentals of Micro-Optics (Cambridge University, 2010).
    [Crossref]
  9. A. Glasmann, T. Hubbard, and E. Bellotti, “Numerical modeling of a dark current suppression mechanism in IR detector arrays,” Proc. SPIE 10177, 101770A (2017).
    [Crossref]
  10. J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
    [Crossref]
  11. J. Schuster and E. Bellotti, “Numerical simulation of crosstalk in reduced pitch HgCdTe photon–trapping structure pixel arrays,” Opt. Express 21(12), 14712–14727 (2013).
    [Crossref] [PubMed]
  12. O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
    [Crossref]
  13. B. Pinkie and E. Bellotti, “Large-scale numerical simulation of reduced-pitch HgCdTe infrared detector arrays,” Proc. SPIE 8704, 87042S (2013).
    [Crossref]
  14. G. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).
    [Crossref]
  15. P. Vaveliuk, B. Ruiz, and A. Lencina, “Limits of the paraxial approximation in laser beams,” Opt. Lett. 32(8), 927–929 (2007).
    [Crossref] [PubMed]
  16. J. Verdeyen, Laser Electronics (Prentice Hall, 1995), Chap. 3.

2017 (1)

A. Glasmann, T. Hubbard, and E. Bellotti, “Numerical modeling of a dark current suppression mechanism in IR detector arrays,” Proc. SPIE 10177, 101770A (2017).
[Crossref]

2014 (3)

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

A. R. Wichman, R. E. DeWames, and E. Bellotti, “Three-dimensional numerical simulation of planar P+n heterojunction In0.53Ga0.47As photodiodes in dense arrays part I: dark current dependence on device geometry,” Proc. SPIE 9070, 907003 (2014).
[Crossref]

2013 (2)

B. Pinkie and E. Bellotti, “Large-scale numerical simulation of reduced-pitch HgCdTe infrared detector arrays,” Proc. SPIE 8704, 87042S (2013).
[Crossref]

J. Schuster and E. Bellotti, “Numerical simulation of crosstalk in reduced pitch HgCdTe photon–trapping structure pixel arrays,” Opt. Express 21(12), 14712–14727 (2013).
[Crossref] [PubMed]

2012 (4)

A. Zemel, U. Mizrahi, and T. Fishman, “Nondestructive measurement of the minority carrier diffusion length in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 101, 133501 (2012).
[Crossref]

G. C. Holst and R. G. Driggers, “Small detectors in infrared system design,” Opt. Eng. 51(9), 096401 (2012).
[Crossref]

R. G. Driggers, R. H. Vollmerhausen, J. P. Reynolds, J. D. Fanning, and G. C. Holst, “Infrared detector size: how low should you go?” Opt. Eng. 51(6), 063202 (2012).
[Crossref]

H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
[Crossref]

2007 (2)

1988 (1)

M. Gallant and A. Zemel, “Long minority hole diffusion length and evidence for bulk radiative recombination limited lifetime in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 52, 1686 (1988).
[Crossref]

Bai, J.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Baier, N.

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

Bellotti, E.

A. Glasmann, T. Hubbard, and E. Bellotti, “Numerical modeling of a dark current suppression mechanism in IR detector arrays,” Proc. SPIE 10177, 101770A (2017).
[Crossref]

A. R. Wichman, R. E. DeWames, and E. Bellotti, “Three-dimensional numerical simulation of planar P+n heterojunction In0.53Ga0.47As photodiodes in dense arrays part I: dark current dependence on device geometry,” Proc. SPIE 9070, 907003 (2014).
[Crossref]

B. Pinkie and E. Bellotti, “Large-scale numerical simulation of reduced-pitch HgCdTe infrared detector arrays,” Proc. SPIE 8704, 87042S (2013).
[Crossref]

J. Schuster and E. Bellotti, “Numerical simulation of crosstalk in reduced pitch HgCdTe photon–trapping structure pixel arrays,” Opt. Express 21(12), 14712–14727 (2013).
[Crossref] [PubMed]

Berthoz, J.

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

Bey, P.

H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
[Crossref]

Boreman, G.

G. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).
[Crossref]

Chen, X.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Cluzel, R.

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

DeWames, R. E.

A. R. Wichman, R. E. DeWames, and E. Bellotti, “Three-dimensional numerical simulation of planar P+n heterojunction In0.53Ga0.47As photodiodes in dense arrays part I: dark current dependence on device geometry,” Proc. SPIE 9070, 907003 (2014).
[Crossref]

Driggers, R. G.

G. C. Holst and R. G. Driggers, “Small detectors in infrared system design,” Opt. Eng. 51(9), 096401 (2012).
[Crossref]

R. G. Driggers, R. H. Vollmerhausen, J. P. Reynolds, J. D. Fanning, and G. C. Holst, “Infrared detector size: how low should you go?” Opt. Eng. 51(6), 063202 (2012).
[Crossref]

Fanning, J. D.

R. G. Driggers, R. H. Vollmerhausen, J. P. Reynolds, J. D. Fanning, and G. C. Holst, “Infrared detector size: how low should you go?” Opt. Eng. 51(6), 063202 (2012).
[Crossref]

Ferron, A.

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

Fishman, T.

A. Zemel, U. Mizrahi, and T. Fishman, “Nondestructive measurement of the minority carrier diffusion length in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 101, 133501 (2012).
[Crossref]

Gallant, M.

M. Gallant and A. Zemel, “Long minority hole diffusion length and evidence for bulk radiative recombination limited lifetime in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 52, 1686 (1988).
[Crossref]

Glasmann, A.

A. Glasmann, T. Hubbard, and E. Bellotti, “Numerical modeling of a dark current suppression mechanism in IR detector arrays,” Proc. SPIE 10177, 101770A (2017).
[Crossref]

Gravrand, O.

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

Guo, N.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Holst, G. C.

R. G. Driggers, R. H. Vollmerhausen, J. P. Reynolds, J. D. Fanning, and G. C. Holst, “Infrared detector size: how low should you go?” Opt. Eng. 51(6), 063202 (2012).
[Crossref]

G. C. Holst and R. G. Driggers, “Small detectors in infrared system design,” Opt. Eng. 51(9), 096401 (2012).
[Crossref]

G. C. Holst, “Imaging system performance based upon Fλ/d,” Opt. Eng. 46(10), 103204 (2007).
[Crossref]

Hu, W.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Hubbard, T.

A. Glasmann, T. Hubbard, and E. Bellotti, “Numerical modeling of a dark current suppression mechanism in IR detector arrays,” Proc. SPIE 10177, 101770A (2017).
[Crossref]

Kilmer, L. C.

H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
[Crossref]

Kimchi, J.

H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
[Crossref]

Lei, W.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Lencina, A.

Lu, W.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Lv, Y.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Meixell, M.

H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
[Crossref]

Mizrahi, U.

A. Zemel, U. Mizrahi, and T. Fishman, “Nondestructive measurement of the minority carrier diffusion length in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 101, 133501 (2012).
[Crossref]

Pinkie, B.

B. Pinkie and E. Bellotti, “Large-scale numerical simulation of reduced-pitch HgCdTe infrared detector arrays,” Proc. SPIE 8704, 87042S (2013).
[Crossref]

Reynolds, J. P.

R. G. Driggers, R. H. Vollmerhausen, J. P. Reynolds, J. D. Fanning, and G. C. Holst, “Infrared detector size: how low should you go?” Opt. Eng. 51(6), 063202 (2012).
[Crossref]

Rochette, F.

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

Rubaldo, L.

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

Ruiz, B.

Schuster, J.

Si, J.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Vaveliuk, P.

Verdeyen, J.

J. Verdeyen, Laser Electronics (Prentice Hall, 1995), Chap. 3.

Vollmerhausen, R. H.

R. G. Driggers, R. H. Vollmerhausen, J. P. Reynolds, J. D. Fanning, and G. C. Holst, “Infrared detector size: how low should you go?” Opt. Eng. 51(6), 063202 (2012).
[Crossref]

Wichman, A. R.

A. R. Wichman, R. E. DeWames, and E. Bellotti, “Three-dimensional numerical simulation of planar P+n heterojunction In0.53Ga0.47As photodiodes in dense arrays part I: dark current dependence on device geometry,” Proc. SPIE 9070, 907003 (2014).
[Crossref]

Yuan, H.

H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
[Crossref]

Zappe, H.

H. Zappe, Fundamentals of Micro-Optics (Cambridge University, 2010).
[Crossref]

Zemel, A.

A. Zemel, U. Mizrahi, and T. Fishman, “Nondestructive measurement of the minority carrier diffusion length in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 101, 133501 (2012).
[Crossref]

M. Gallant and A. Zemel, “Long minority hole diffusion length and evidence for bulk radiative recombination limited lifetime in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 52, 1686 (1988).
[Crossref]

Zhang, J.

H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
[Crossref]

Zhang, X.

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

Appl. Phys. Lett. (2)

M. Gallant and A. Zemel, “Long minority hole diffusion length and evidence for bulk radiative recombination limited lifetime in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 52, 1686 (1988).
[Crossref]

A. Zemel, U. Mizrahi, and T. Fishman, “Nondestructive measurement of the minority carrier diffusion length in InP/InGaAs/InP double heterostructures,” Appl. Phys. Lett. 101, 133501 (2012).
[Crossref]

J. Electron. Mater. (2)

J. Bai, W. Hu, N. Guo, W. Lei, Y. Lv, X. Zhang, J. Si, X. Chen, and W. Lu, “Performance optimization of InSb infrared focal-plane arrays with diffractive microlenses,” J. Electron. Mater. 43(8), 2795–2801 (2014).
[Crossref]

O. Gravrand, N. Baier, A. Ferron, F. Rochette, J. Berthoz, L. Rubaldo, and R. Cluzel, “MTF Issues in Small-Pixel-Pitch Planar Quantum IR Detectors,” J. Electron. Mater. 43(8), 3025–3032 (2014).
[Crossref]

Opt. Eng. (3)

G. C. Holst, “Imaging system performance based upon Fλ/d,” Opt. Eng. 46(10), 103204 (2007).
[Crossref]

G. C. Holst and R. G. Driggers, “Small detectors in infrared system design,” Opt. Eng. 51(9), 096401 (2012).
[Crossref]

R. G. Driggers, R. H. Vollmerhausen, J. P. Reynolds, J. D. Fanning, and G. C. Holst, “Infrared detector size: how low should you go?” Opt. Eng. 51(6), 063202 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (4)

B. Pinkie and E. Bellotti, “Large-scale numerical simulation of reduced-pitch HgCdTe infrared detector arrays,” Proc. SPIE 8704, 87042S (2013).
[Crossref]

A. Glasmann, T. Hubbard, and E. Bellotti, “Numerical modeling of a dark current suppression mechanism in IR detector arrays,” Proc. SPIE 10177, 101770A (2017).
[Crossref]

H. Yuan, M. Meixell, J. Zhang, P. Bey, J. Kimchi, and L. C. Kilmer, “Low dark current small pixel large format InGaAs 2D photodetector array development at Teledyne Judson Technologies,” Proc. SPIE 8353, 835309 (2012).
[Crossref]

A. R. Wichman, R. E. DeWames, and E. Bellotti, “Three-dimensional numerical simulation of planar P+n heterojunction In0.53Ga0.47As photodiodes in dense arrays part I: dark current dependence on device geometry,” Proc. SPIE 9070, 907003 (2014).
[Crossref]

Other (3)

H. Zappe, Fundamentals of Micro-Optics (Cambridge University, 2010).
[Crossref]

G. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).
[Crossref]

J. Verdeyen, Laser Electronics (Prentice Hall, 1995), Chap. 3.

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Figures (13)

Fig. 1
Fig. 1 Two-dimensional structure of the detector array with baseline dimensions and doping concentrations. The structure is shown with its illuminated side (backside of the N-InP substrate) facing up. Microlenses are pictured but are not part of the baseline structure. On the substrate resides a double layer planar heterostructure consisting of an n-InGaAs absorber of thickness t and an N-InP cap. Rectangular p+ diffusions are drawn as shaded regions. Three pixels are shown with pitch d and nominal footprints rj (also of with d). For optical simulations, this structure is surrounded by vacuum.
Fig. 2
Fig. 2 Left: spot scan profiles for baseline array configurations with pitches 12, 6, and 4 µm and no microlenses. Photocurrent is normalized to one. Ideal spot scan curves which correspond to an ideal MTF are also shown for the largest and smallest pitch. Right: corresponding modulation transfer functions relative to the ideal MTF given by Eq. (4). Spatial frequency is normalized for each array by their respective cutoff frequency of 1/d.
Fig. 3
Fig. 3 Comparison of the electric field and optical generation rates in the substrate and absorber regions for a 12 µm pitch array (a) without microlenses and (b) with microlenses. In the substrate regions (y > 0), the squared magnitude of electric field (|E|2) is shown. In the absorber (y < 0), optical generation rate (G opt) is shown. Plane wave illumination of wavelength 1 µm and flux density 1 × 1012 cm−2s−1 is used.
Fig. 4
Fig. 4 Squared magnitude of the electric field (|E|2) in the substrate and absorber regions as a Gaussian beam with w0 = 3 µm is swept across a 6 µm pitch array with microlenses. The waist of the Gaussian beam begins at a pixel center (a) and is swept toward the right edge of the array in 1 µm steps (b)–(f). In order to collect a spot scan profile, the photocurrent of a pixel is simulated as a function of the distance between that pixel’s center and the lateral center of the beam waist. The peak irradiance of the beam corresponds to a photon flux density of 1 × 1012 cm−2s−1.
Fig. 5
Fig. 5 Left: spot scan profiles for 12, 6, and 4 µm arrays with microlenses. Ideal spot scans are also shown for the 12 and 4 µm arrays. The spot scan curve for the 12 µm array lies on top of the corresponding ideal curve for the majority of the profile. Right: corresponding MTFs. For each array, the addition of microlenses brings the response closer to ideal performance, particularly for spatial frequencies near the cutoff.
Fig. 6
Fig. 6 Left: MTF results for a 4 µm pitch array with microlenses and varying absorber thickness (t). Right: the same, for an array pitch of 6 µm. For both pitches, reducing the absorber thickness moves the response closer to the ideal.
Fig. 7
Fig. 7 Profiles of photogenerated hole concentration (p′) for a 12 µm pitch array in the absorber region for thicknesses of (a) 3 and (b) 1.5 µm. The absorber-substrate interface lies at y = 0. This array has no lenses and is illuminated from the top with a Gaussian beam of w0 = 3 µm that is centered on the middle pixel.
Fig. 8
Fig. 8 Left: dark current as a function of absorber thickness for 12, 6, and 4 µm pitch arrays. Dark current is expressed in picoamps per centimeter of array depth in the third dimension. Right: quantum efficiency for the same arrays, with and without microlenses. Quantum efficiency is uncorrected for reflection of the plane wave illumination. The reflectance at the vacuum–InP interface has an average value of 31%.
Fig. 9
Fig. 9 Left: MTF results for a 4 µm pitch array with microlenses and varying doping concentration in the absorber (ND, abs). Right: the same, for an array pitch of 6 µm. For both pitches, the best MTF results are achieved for doping concentrations of 1 × 1015 cm−3 and 1 × 1018 cm3. The baseline doping concentration of 1 × 1016 cm−3 is comparable to the 1 × 1017 cm−3 case and these variants provide a less ideal response.
Fig. 10
Fig. 10 Band profile in the InGaAs absorber for the 6 µm pitch array for various doping concentrations at thermal equilibrium. The bands are plotted for a vertical slice in the x-direction through a pixel center. The substrate side of the absorber lies at y = 0 µm. The sensing junction lies at y = 2.8 µm. The Fermi energy is fixed at 0 eV. As doping concentration is increased, the portion of this slice in which there is a significant electric field (as indicated by band bending) decreases.
Fig. 11
Fig. 11 Profiles of photogenerated hole concentration (p′) in the absorber for doping concentrations of (a) 1 × 1015, (b) 1 × 1016, and (c) 1 × 1018 cm−3. The absorber-substrate interface lies at y = 0. This array has no lenses and is illuminated from the top with a Gaussian beam of w0 = 3 µm that is centered on the middle pixel.
Fig. 12
Fig. 12 Left: dark current as a function of doping concentration in the absorber for the 4, 6, and 12 µm pitch arrays. Dark current is expressed in picoamps per centimeter of array depth in the third dimension. Right: quantum efficiency for the same arrays, with and without microlenses. Quantum efficiency is uncorrected for reflection of the plane wave illumination. The reflectance at the vacuum–InP interface has an average value of 31%.
Fig. 13
Fig. 13 Total generation rate the InGaAs absorber for the 6 µm pitch array for various doping concentrations under reverse bias. The rates are plotted for a slice in the y-direction through a pixel center. The substrate side of the absorber lies at y = 0 µm. The sensing junction lies at y = 2.8 µm. The total generation is a sum of SRH, radiative, and Auger rates.

Tables (1)

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Table 1 Overview of values varied in the parametric study of the MTF

Equations (8)

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n 0 S o + n L S i = 1 R ( n L n 0 ) ,
f = R n L ( λ ) 1 + ( R 2 d 2 / 4 ) 1 / 2 .
OTF H ( ξ , η ) = | H ( ξ , η ) | e j θ ( ξ , η ) .
MTF ideal ( ξ ) = sin ( π d ξ ) π d ξ .
g ( x ) = I 0 exp ( 2 r 2 w 0 2 ) ,
[ footprint ] = [ SS generation ( x ) ] [ g ( x ) ] ,
MTF ideal ( ξ ) MTF optical ( ξ ) = | [ SS generation ( x ) ] [ g ( x ) ] | ,
MTF ideal ( ξ ) MTF optical ( ξ ) MTF diffusion ( ξ ) = | [ SS photocurrent ( x ) ] [ g ( x ) ] | ,

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