Abstract

We discuss in detail the physics of light emission from porous silicon microcavities formed by periodically modulating the porosity to produce multilayered structures. Changing the porosity alters not only the refractive index and absorption but also the luminescence, resulting in a complex interplay of effects that has not yet been addressed in the literature as far as we know. A transfer matrix model is developed that accounts for the dispersion of the refractive index, absorption, and photoluminescence. A multilayer porous silicon mirror is found to emit light almost as well as a conventional distributed feedback microcavity system with a mid-stop-band resonant state.

© 1998 Optical Society of America

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  1. L. T. Canham, “Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers,” Appl. Phys. Lett. 57, 1046–1048 (1990).
    [CrossRef]
  2. N. Koshida, H. Koyama, “Visible electroluminescence from porous silicon,” Appl. Phys. Lett. 60, 347–349 (1992).
    [CrossRef]
  3. A. Loni, A. J. Simons, T. I. Cox, P. D. J. Calcott, L. T. Canham, “Electroluminescent porous silicon device with an external quantum efficiency of greater than 0.1% under CW operation,” Electron. Lett. 31, 1288–1289 (1995).
    [CrossRef]
  4. L. Pavesi, R. Guardini, C. Mazzoleni, “Porous silicon resonant cavity light emitting diodes,” Solid State Commun. 97, 1051–1053 (1996).
    [CrossRef]
  5. M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
    [CrossRef]
  6. M. Araki, H. Koyama, N. Koshida, “Precisely tuned emission from porous silicon vertical optical cavity in the visible region,” J. Appl. Phys. 80, 4841–4844 (1996).
    [CrossRef]
  7. G. Lérondel, P. Ferrand, R. Romestain, “Elaboration and light emission properties of low doped P-type porous silicon microcavities,” Mater. Res. Soc. Symp. Proc. 452, 711–716 (1997).
    [CrossRef]
  8. P. St. J. Russell, T. A. Birks, F. Dominic Lloyd-Lucas, Confined Electrons and Photons (Plenum, New York, 1995), pp. 585–633.
    [CrossRef]
  9. C. D. Salzberg, “Infrared refractive indexes of silicon germanium and modified selenium glass,” J. Opt. Soc. Am. 47, 244–246 (1957).
    [CrossRef]
  10. A = 3.41696, B = 0.138497 μm2, C = 0.013924 μm4, D = -2.09 × 10-5 μm-2, E = 1.48 × 10-7 μm-4, F = 0.028 μm2.
  11. D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. (Leipzig) 24, 636–664 (1935).
  12. L. Pavesi, C. Mazzoleni, A. Tredicucci, V. Pellegrini, “Controlled photon emission in porous silicon microcavities,” Appl. Phys. Lett. 67, 3280–3282 (1995).
    [CrossRef]
  13. E. D. Palik, ed., Handbook of Optical Constants in Solids (Academic, New York, 1991), pp. 564–566.

1997

G. Lérondel, P. Ferrand, R. Romestain, “Elaboration and light emission properties of low doped P-type porous silicon microcavities,” Mater. Res. Soc. Symp. Proc. 452, 711–716 (1997).
[CrossRef]

1996

M. Araki, H. Koyama, N. Koshida, “Precisely tuned emission from porous silicon vertical optical cavity in the visible region,” J. Appl. Phys. 80, 4841–4844 (1996).
[CrossRef]

L. Pavesi, R. Guardini, C. Mazzoleni, “Porous silicon resonant cavity light emitting diodes,” Solid State Commun. 97, 1051–1053 (1996).
[CrossRef]

1995

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

A. Loni, A. J. Simons, T. I. Cox, P. D. J. Calcott, L. T. Canham, “Electroluminescent porous silicon device with an external quantum efficiency of greater than 0.1% under CW operation,” Electron. Lett. 31, 1288–1289 (1995).
[CrossRef]

L. Pavesi, C. Mazzoleni, A. Tredicucci, V. Pellegrini, “Controlled photon emission in porous silicon microcavities,” Appl. Phys. Lett. 67, 3280–3282 (1995).
[CrossRef]

1992

N. Koshida, H. Koyama, “Visible electroluminescence from porous silicon,” Appl. Phys. Lett. 60, 347–349 (1992).
[CrossRef]

1990

L. T. Canham, “Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers,” Appl. Phys. Lett. 57, 1046–1048 (1990).
[CrossRef]

1957

1935

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. (Leipzig) 24, 636–664 (1935).

Araki, M.

M. Araki, H. Koyama, N. Koshida, “Precisely tuned emission from porous silicon vertical optical cavity in the visible region,” J. Appl. Phys. 80, 4841–4844 (1996).
[CrossRef]

Arens-Fischer, R.

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

Arntzen, M.

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

Berger, M. G.

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

Birks, T. A.

P. St. J. Russell, T. A. Birks, F. Dominic Lloyd-Lucas, Confined Electrons and Photons (Plenum, New York, 1995), pp. 585–633.
[CrossRef]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. (Leipzig) 24, 636–664 (1935).

Calcott, P. D. J.

A. Loni, A. J. Simons, T. I. Cox, P. D. J. Calcott, L. T. Canham, “Electroluminescent porous silicon device with an external quantum efficiency of greater than 0.1% under CW operation,” Electron. Lett. 31, 1288–1289 (1995).
[CrossRef]

Canham, L. T.

A. Loni, A. J. Simons, T. I. Cox, P. D. J. Calcott, L. T. Canham, “Electroluminescent porous silicon device with an external quantum efficiency of greater than 0.1% under CW operation,” Electron. Lett. 31, 1288–1289 (1995).
[CrossRef]

L. T. Canham, “Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers,” Appl. Phys. Lett. 57, 1046–1048 (1990).
[CrossRef]

Cox, T. I.

A. Loni, A. J. Simons, T. I. Cox, P. D. J. Calcott, L. T. Canham, “Electroluminescent porous silicon device with an external quantum efficiency of greater than 0.1% under CW operation,” Electron. Lett. 31, 1288–1289 (1995).
[CrossRef]

Dominic Lloyd-Lucas, F.

P. St. J. Russell, T. A. Birks, F. Dominic Lloyd-Lucas, Confined Electrons and Photons (Plenum, New York, 1995), pp. 585–633.
[CrossRef]

Ferrand, P.

G. Lérondel, P. Ferrand, R. Romestain, “Elaboration and light emission properties of low doped P-type porous silicon microcavities,” Mater. Res. Soc. Symp. Proc. 452, 711–716 (1997).
[CrossRef]

Guardini, R.

L. Pavesi, R. Guardini, C. Mazzoleni, “Porous silicon resonant cavity light emitting diodes,” Solid State Commun. 97, 1051–1053 (1996).
[CrossRef]

Koshida, N.

M. Araki, H. Koyama, N. Koshida, “Precisely tuned emission from porous silicon vertical optical cavity in the visible region,” J. Appl. Phys. 80, 4841–4844 (1996).
[CrossRef]

N. Koshida, H. Koyama, “Visible electroluminescence from porous silicon,” Appl. Phys. Lett. 60, 347–349 (1992).
[CrossRef]

Koyama, H.

M. Araki, H. Koyama, N. Koshida, “Precisely tuned emission from porous silicon vertical optical cavity in the visible region,” J. Appl. Phys. 80, 4841–4844 (1996).
[CrossRef]

N. Koshida, H. Koyama, “Visible electroluminescence from porous silicon,” Appl. Phys. Lett. 60, 347–349 (1992).
[CrossRef]

Lérondel, G.

G. Lérondel, P. Ferrand, R. Romestain, “Elaboration and light emission properties of low doped P-type porous silicon microcavities,” Mater. Res. Soc. Symp. Proc. 452, 711–716 (1997).
[CrossRef]

Loni, A.

A. Loni, A. J. Simons, T. I. Cox, P. D. J. Calcott, L. T. Canham, “Electroluminescent porous silicon device with an external quantum efficiency of greater than 0.1% under CW operation,” Electron. Lett. 31, 1288–1289 (1995).
[CrossRef]

Lüth, H.

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

Mazzoleni, C.

L. Pavesi, R. Guardini, C. Mazzoleni, “Porous silicon resonant cavity light emitting diodes,” Solid State Commun. 97, 1051–1053 (1996).
[CrossRef]

L. Pavesi, C. Mazzoleni, A. Tredicucci, V. Pellegrini, “Controlled photon emission in porous silicon microcavities,” Appl. Phys. Lett. 67, 3280–3282 (1995).
[CrossRef]

Münder, H.

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

Pavesi, L.

L. Pavesi, R. Guardini, C. Mazzoleni, “Porous silicon resonant cavity light emitting diodes,” Solid State Commun. 97, 1051–1053 (1996).
[CrossRef]

L. Pavesi, C. Mazzoleni, A. Tredicucci, V. Pellegrini, “Controlled photon emission in porous silicon microcavities,” Appl. Phys. Lett. 67, 3280–3282 (1995).
[CrossRef]

Pellegrini, V.

L. Pavesi, C. Mazzoleni, A. Tredicucci, V. Pellegrini, “Controlled photon emission in porous silicon microcavities,” Appl. Phys. Lett. 67, 3280–3282 (1995).
[CrossRef]

Romestain, R.

G. Lérondel, P. Ferrand, R. Romestain, “Elaboration and light emission properties of low doped P-type porous silicon microcavities,” Mater. Res. Soc. Symp. Proc. 452, 711–716 (1997).
[CrossRef]

Salzberg, C. D.

Simons, A. J.

A. Loni, A. J. Simons, T. I. Cox, P. D. J. Calcott, L. T. Canham, “Electroluminescent porous silicon device with an external quantum efficiency of greater than 0.1% under CW operation,” Electron. Lett. 31, 1288–1289 (1995).
[CrossRef]

St. J. Russell, P.

P. St. J. Russell, T. A. Birks, F. Dominic Lloyd-Lucas, Confined Electrons and Photons (Plenum, New York, 1995), pp. 585–633.
[CrossRef]

Theiss, W.

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

Thönissen, M.

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

Tredicucci, A.

L. Pavesi, C. Mazzoleni, A. Tredicucci, V. Pellegrini, “Controlled photon emission in porous silicon microcavities,” Appl. Phys. Lett. 67, 3280–3282 (1995).
[CrossRef]

Ann. Phys. (Leipzig)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. (Leipzig) 24, 636–664 (1935).

Appl. Phys. Lett.

L. Pavesi, C. Mazzoleni, A. Tredicucci, V. Pellegrini, “Controlled photon emission in porous silicon microcavities,” Appl. Phys. Lett. 67, 3280–3282 (1995).
[CrossRef]

L. T. Canham, “Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers,” Appl. Phys. Lett. 57, 1046–1048 (1990).
[CrossRef]

N. Koshida, H. Koyama, “Visible electroluminescence from porous silicon,” Appl. Phys. Lett. 60, 347–349 (1992).
[CrossRef]

Electron. Lett.

A. Loni, A. J. Simons, T. I. Cox, P. D. J. Calcott, L. T. Canham, “Electroluminescent porous silicon device with an external quantum efficiency of greater than 0.1% under CW operation,” Electron. Lett. 31, 1288–1289 (1995).
[CrossRef]

J. Appl. Phys.

M. Araki, H. Koyama, N. Koshida, “Precisely tuned emission from porous silicon vertical optical cavity in the visible region,” J. Appl. Phys. 80, 4841–4844 (1996).
[CrossRef]

J. Opt. Soc. Am.

Mater. Res. Soc. Symp. Proc.

G. Lérondel, P. Ferrand, R. Romestain, “Elaboration and light emission properties of low doped P-type porous silicon microcavities,” Mater. Res. Soc. Symp. Proc. 452, 711–716 (1997).
[CrossRef]

Solid State Commun.

L. Pavesi, R. Guardini, C. Mazzoleni, “Porous silicon resonant cavity light emitting diodes,” Solid State Commun. 97, 1051–1053 (1996).
[CrossRef]

Thin Solid Films

M. G. Berger, M. Thönissen, R. Arens-Fischer, H. Münder, H. Lüth, M. Arntzen, W. Theiss, “Investigation and design of optical properties of porosity superlattices,” Thin Solid Films 255, 313–316 (1995).
[CrossRef]

Other

P. St. J. Russell, T. A. Birks, F. Dominic Lloyd-Lucas, Confined Electrons and Photons (Plenum, New York, 1995), pp. 585–633.
[CrossRef]

A = 3.41696, B = 0.138497 μm2, C = 0.013924 μm4, D = -2.09 × 10-5 μm-2, E = 1.48 × 10-7 μm-4, F = 0.028 μm2.

E. D. Palik, ed., Handbook of Optical Constants in Solids (Academic, New York, 1991), pp. 564–566.

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Figures (5)

Fig. 1
Fig. 1

Comparison of p-Si structures: (a) a single 75% porosity layer, (b) a multilayer stack with layer porosities of 75% and 64%, (c) a microcavity structure composed of a central λ/2 75% porosity defect between two multilayer stacks.

Fig. 2
Fig. 2

(a) Reflectivity (R) and transmissivity (T) of a single 75% porosity layer of a 2.86-μm width with no gain. The Gaussian gain profile is also shown, with the single layer emission peak indicated by a dotted line. (b) Sum of reflectivity and transmissivity of the same layer but with added gain. Curves a, b, c, and d correspond to gains of 1.2, 2.3, 2.9, and 3.5 μm-1.

Fig. 3
Fig. 3

(a) Reflectivity (R) and transmissivity (T) of a 39-multilayer stack designed so that the first Fabry–Perot resonance on the high-frequency side of the stop band sits on the gain peak. The gain peak remains in the same position as that shown in Fig. 2. The layer widths are 0.14 μm (low index) and 0.12 μm (high index). (b) Sum of reflectivity and transmissivity with added gain. Curves a, b, and c correspond to gains of 0, 0.06, and 0.12 μm-1.

Fig. 4
Fig. 4

(a) Reflectivity (R) and transmissivity (T) of a 39-multilayer stack designed so that the first Fabry–Perot resonance on the low-frequency side of the stop band sits on the gain peak. The layer widths are 0.14 μm (low index) and 0.08 μm (high index). (b) Sum of reflectivity and transmissivity with added gain. Curves a, b, and c correspond to gains of 0, 0.16, and 0.35 μm-1.

Fig. 5
Fig. 5

(a) Reflectivity (R) and transmissivity (T) of a microcavity consisting of a λ/2 thick layer of emitting material between two 20-layer multilayer stacks; note the cavity mode in the middle of the stop band. The layer widths are 0.26 μm (defect layer), 0.13 μm (low index), and 0.11 μm (high index). (b) The sum of reflectivity and transmission with added gain. Curves a, b, and c correspond to gains of 0, 0.05, and 0.10 μm-1.

Tables (1)

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Table 1 Summary of Results

Equations (7)

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n s λ = A + BL + CL 2 + D λ 2 + E λ 4 ,
f a a - a + 2 + 1 - f a s - s + 2 = 0 ,
n L = L + i n α λ - λ g λ / 4 π ,
n H = H + i n α λ ,
g λ = g 0 exp - 0.5 λ - λ 0 / Δ λ 2 ,
n α = 0.815   exp - λ - 0.3827 0.6398 0.1027 f S ,
λ B = 2 n L d L + n H d H ,

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