Abstract

We investigate the possibility of recovering spectral information using a multilayer structure realized through microelectronics technologies and compatible with a matrix arrangement. The structure is made of photoabsorbing layers, acting as local photodetectors, alternating with transparent layers. The whole structure lies on a reflective surface. A stationary wave containing the spectral information of the source is generated within the structure. We determine the intensity of the stationary wave at any position, taking into account absorption and multireflections at each transition as well as the signal detected by the photoabsorbing layers. The model forecasting the detected signal is then validated using p-i-n diodes of different thicknesses made of hydrogenated amorphous silicon (a-Si:H) encompassed between indium tin oxide (ITO) electrodes. The detected signal depends on the wavelength of the incident light, the thickness of the detecting layer, and the latter’s position within the structure. A specific spectral response can then be associated to each photoabsorbing layer. We show how spectral information can be retrieved from this kind of structure in the visible spectrum range.

© 2009 Optical Society of America

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  1. R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197-202 (2004).
    [CrossRef]
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    [CrossRef]
  3. D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
    [CrossRef]
  4. H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
    [CrossRef]
  5. P. Parrein, A. Landragin-Frassati, and J.-M. Dinten, “Reconstruction method and optimal design of interferometric spectrometer,” Appl. Spectrosc., document ID 08-05318 (to be published).
  6. M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).
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  8. K. Ohta and H. Ishida, “Matrix formalism for calculation of electric field intensity of light in stratified multilayered films,” Appl. Opt. 29, 1952-1959 (1990).
    [CrossRef] [PubMed]
  9. S. Gupta, B. R. Weiner, and G. Morell, “Interplay of hydrogen and deposition temperature in optical properties of hot-wire deposited a-Si:H film: ex situ spectroscopic ellipsometry studies,” J. Vac. Sci. Technol. A 23, 1668-1675 (2005).
    [CrossRef]
  10. D. Daineka, V. Suendo, P. Roca, and I. Cabarrocas, “Temperature dependence of the optical functions of amorphous silicon based materials: application to in situ temperature measurements by spectroscopic ellipsometry,” Thin Solid Films 468, 298-302 (2004).
    [CrossRef]

2007 (1)

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

2005 (2)

D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
[CrossRef]

S. Gupta, B. R. Weiner, and G. Morell, “Interplay of hydrogen and deposition temperature in optical properties of hot-wire deposited a-Si:H film: ex situ spectroscopic ellipsometry studies,” J. Vac. Sci. Technol. A 23, 1668-1675 (2005).
[CrossRef]

2004 (2)

D. Daineka, V. Suendo, P. Roca, and I. Cabarrocas, “Temperature dependence of the optical functions of amorphous silicon based materials: application to in situ temperature measurements by spectroscopic ellipsometry,” Thin Solid Films 468, 298-302 (2004).
[CrossRef]

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197-202 (2004).
[CrossRef]

2003 (1)

H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
[CrossRef]

1990 (1)

1948 (1)

F. Abelès, “Sur la propagation des ondes electromagnétiques dans les milieux stratifies,” Ann. Phys. (Paris) 3, 504-520(1948).

Abelès, F.

F. Abelès, “Sur la propagation des ondes electromagnétiques dans les milieux stratifies,” Ann. Phys. (Paris) 3, 504-520(1948).

Benech, P.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Bhalotra, S. R.

D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
[CrossRef]

Blaize, S.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Büchner, H. J.

H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
[CrossRef]

Bunte, E.

D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
[CrossRef]

H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
[CrossRef]

Cabarrocas, I.

D. Daineka, V. Suendo, P. Roca, and I. Cabarrocas, “Temperature dependence of the optical functions of amorphous silicon based materials: application to in situ temperature measurements by spectroscopic ellipsometry,” Thin Solid Films 468, 298-302 (2004).
[CrossRef]

Cloarer, E. Le

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Daineka, D.

D. Daineka, V. Suendo, P. Roca, and I. Cabarrocas, “Temperature dependence of the optical functions of amorphous silicon based materials: application to in situ temperature measurements by spectroscopic ellipsometry,” Thin Solid Films 468, 298-302 (2004).
[CrossRef]

Dinten, J.-M.

P. Parrein, A. Landragin-Frassati, and J.-M. Dinten, “Reconstruction method and optimal design of interferometric spectrometer,” Appl. Spectrosc., document ID 08-05318 (to be published).

Fedeli, J.-M.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Gupta, S.

S. Gupta, B. R. Weiner, and G. Morell, “Interplay of hydrogen and deposition temperature in optical properties of hot-wire deposited a-Si:H film: ex situ spectroscopic ellipsometry studies,” J. Vac. Sci. Technol. A 23, 1668-1675 (2005).
[CrossRef]

Ishida, H.

Jäger, G.

H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
[CrossRef]

Kern, P.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Knipp, D.

D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
[CrossRef]

H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
[CrossRef]

Kung, H. L.

D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
[CrossRef]

Landragin-Frassati, A.

P. Parrein, A. Landragin-Frassati, and J.-M. Dinten, “Reconstruction method and optimal design of interferometric spectrometer,” Appl. Spectrosc., document ID 08-05318 (to be published).

Leblond, G.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Lérondel, G.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Mandryka, V.

H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
[CrossRef]

Miller, D. A. B.

D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
[CrossRef]

Morand, A.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Morell, G.

S. Gupta, B. R. Weiner, and G. Morell, “Interplay of hydrogen and deposition temperature in optical properties of hot-wire deposited a-Si:H film: ex situ spectroscopic ellipsometry studies,” J. Vac. Sci. Technol. A 23, 1668-1675 (2005).
[CrossRef]

Ohta, K.

Parrein, P.

P. Parrein, A. Landragin-Frassati, and J.-M. Dinten, “Reconstruction method and optimal design of interferometric spectrometer,” Appl. Spectrosc., document ID 08-05318 (to be published).

Roca, P.

D. Daineka, V. Suendo, P. Roca, and I. Cabarrocas, “Temperature dependence of the optical functions of amorphous silicon based materials: application to in situ temperature measurements by spectroscopic ellipsometry,” Thin Solid Films 468, 298-302 (2004).
[CrossRef]

Royer, P.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Stefanon, I.

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Steibig, H.

D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
[CrossRef]

H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
[CrossRef]

Suendo, V.

D. Daineka, V. Suendo, P. Roca, and I. Cabarrocas, “Temperature dependence of the optical functions of amorphous silicon based materials: application to in situ temperature measurements by spectroscopic ellipsometry,” Thin Solid Films 468, 298-302 (2004).
[CrossRef]

Weiner, B. R.

S. Gupta, B. R. Weiner, and G. Morell, “Interplay of hydrogen and deposition temperature in optical properties of hot-wire deposited a-Si:H film: ex situ spectroscopic ellipsometry studies,” J. Vac. Sci. Technol. A 23, 1668-1675 (2005).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Wolffenbuttel, R. F.

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197-202 (2004).
[CrossRef]

Ann. Phys. (Paris) (1)

F. Abelès, “Sur la propagation des ondes electromagnétiques dans les milieux stratifies,” Ann. Phys. (Paris) 3, 504-520(1948).

Appl. Opt. (1)

IEEE Trans. Electron Devices (1)

D. Knipp, H. Steibig, S. R. Bhalotra, E. Bunte, H. L. Kung, and D. A. B. Miller, “Silicon-based micro-Fourier spectrometer,” IEEE Trans. Electron Devices 52, 419-426 (2005).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197-202 (2004).
[CrossRef]

J. Vac. Sci. Technol. A (1)

S. Gupta, B. R. Weiner, and G. Morell, “Interplay of hydrogen and deposition temperature in optical properties of hot-wire deposited a-Si:H film: ex situ spectroscopic ellipsometry studies,” J. Vac. Sci. Technol. A 23, 1668-1675 (2005).
[CrossRef]

Nat. Photonics (1)

E. Le Cloarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, and P. Royer, “Wavelength-scale stationary wave integrated Fourier-transform spectrometry,” Nat. Photonics 1, 473-478 (2007).
[CrossRef]

Thin Solid Films (2)

D. Daineka, V. Suendo, P. Roca, and I. Cabarrocas, “Temperature dependence of the optical functions of amorphous silicon based materials: application to in situ temperature measurements by spectroscopic ellipsometry,” Thin Solid Films 468, 298-302 (2004).
[CrossRef]

H. Steibig, H. J. Büchner, E. Bunte, V. Mandryka, D. Knipp, and G. Jäger, “Standing wave detection by thin transparent n-i-p diodes of amorphous silicon,” Thin Solid Films 427, 152-156 (2003).
[CrossRef]

Other (2)

P. Parrein, A. Landragin-Frassati, and J.-M. Dinten, “Reconstruction method and optimal design of interferometric spectrometer,” Appl. Spectrosc., document ID 08-05318 (to be published).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

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Figures (11)

Fig. 1
Fig. 1

Scheme of the whole stack.

Fig. 2
Fig. 2

Measurement of the refractive index n.

Fig. 3
Fig. 3

Measurement of the extinction coefficient k.

Fig. 4
Fig. 4

Measured and simulated quantum efficiency of diodes of different thicknesses, measured at 0.2 V , except for the 15 nm diode, which was measured at 0 V .

Fig. 5
Fig. 5

Dark current–voltage characteristic for the thin diodes of 15 nm , 28 nm and 37 nm total thickness.

Fig. 6
Fig. 6

Measured and simulated quantum efficiency of the thin diodes measured at different voltages.

Fig. 7
Fig. 7

An example of narrowband spectrum restitution from data acquired by the seven detecting structures of 7 nm thickness and using the inverse problem-solving and iterative methods.

Fig. 8
Fig. 8

An example of broadband spectrum restitution from data acquired by the seven detecting structures of 7 nm thickness and using the inverse problem-solving and iterative methods.

Fig. 9
Fig. 9

Modeling of the quantum efficiency QE of the detecting structures obtained for a compound of two stacks with three layers on each stack. Each detecting structure has an i layer equal to 7 nm and doped layers of 3 nm . This data is seen as the filter’s spectral responses are used to build up the L matrix.

Fig. 10
Fig. 10

An example of narrowband spectrum restitution from data acquired by the 2 × 3 detecting structures having an intrinsic layer equal to 7 nm and doped layers equal to 3 nm and using the inverse problem-solving and iterative methods.

Fig. 11
Fig. 11

An example of broadband spectrum restitution from data acquired by the 2 × 3 detecting structures having an intrinsic layer equal to 7 nm and doped layers equal to 3 nm and using the inverse problem-solving and iterative methods.

Equations (7)

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

S i ( λ ) = σ 0 e i E i ( λ , z ) E i * ( λ , z ) d z ,
σ = 4 π n k c ε 0 λ .
QE i ( λ ) = 4 π n k λ 0 e i E ˜ i ( λ , z ) E ˜ i * ( λ , z ) d z ,
E ˜ i ( λ , z ) = E i ( λ , z ) E 0 + ( λ ) .
R i = e h c + λ QE i ( λ ) d λ .
x = L s .
s ^ = L x .

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