Abstract

In this study an analytical model that takes into account the coupled photoelastic and thermo-optical effects is established to evaluate the temperature dependence of a single-chip silicon micromachined Fabry–Perot pressure sensor. The results show that temperature variation has a significant effect on the performance of a micromachined Fabry–Perot pressure sensor with a conventional flat diaphragm. A new membrane-type silicon micromachined Fabry–Perot pressure sensor with a novel deeply corrugated diaphragm is then proposed. The sensor is fabricated on a single-chip by use of both surface- and bulk-micromachining techniques. Both analytical and experimental results show that the cross sensitivity of Fabry–Perot pressure sensors to temperature can be substantially alleviated by use of the proposed single deeply corrugated diaphragm.

© 2005 Optical Society of America

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References

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  1. Y. Kim, D. P. Neikirk, “Micromachined Fabry–Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7, 1471–1473 (1995).
    [CrossRef]
  2. D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
    [CrossRef]
  3. J. Han, J. Y. Kim, T. S. Kim, J. S. Kim, “Performance of Fabry–Perot microcavity structures with corrugated diaphragms,” Sens. Actuators A 79, 162–172 (2000).
    [CrossRef]
  4. S. Sakaguchi, “Temperature dependence of transmission characteristics of multilayer film narrow bandpass filters,” Jpn. J. Appl. Phys. 38, 6362–6368 (1999).
    [CrossRef]
  5. A. Zoller, R. Gotzelmann, K. Matl, D. Cushing, “Temperature-stable bandpass filters deposited with plasma ion-assisted deposition,” Appl. Opt. 35, 5609–5612 (1996).
    [CrossRef] [PubMed]
  6. V. L. Spiering, S. Bouwstra, R. M. E. J. Spiering, “On-chip decoupling zone for package-stress reduction,” Sens. Actuators A 39, 149–156 (1993).
    [CrossRef]
  7. W. J. Wang, R. M. Lin, D. G. Guo, “Study of single deeply corrugated diaphragm for high sensitivity microphones,” J. Micromech. Microeng. 13, 184–189 (2003).
    [CrossRef]
  8. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, Bristol, UK, 2001).
    [CrossRef]
  9. H. Aben, C. Guillemet, Photoelasticity of Glass (Springer-Verlag, Berlin, 1993).
    [CrossRef]
  10. T. C. Chen, J. I. Kuo, W. L. Lee, C. C. Lee, “Influences of temperature and stress on transmission characteristics of multilayer thin-film narrow bandpass filters,” Jpn. J. Appl. Phys. 40, 4087–4096 (2001).
    [CrossRef]
  11. W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel non-planar diaphragm,” Microelectron. Eng. 70, 102–108 (2003).
    [CrossRef]
  12. F. I. Niordson, Shell Theory (North-Holland, Amsterdam, 1985).
  13. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).
  14. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

2003 (2)

W. J. Wang, R. M. Lin, D. G. Guo, “Study of single deeply corrugated diaphragm for high sensitivity microphones,” J. Micromech. Microeng. 13, 184–189 (2003).
[CrossRef]

W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel non-planar diaphragm,” Microelectron. Eng. 70, 102–108 (2003).
[CrossRef]

2001 (2)

T. C. Chen, J. I. Kuo, W. L. Lee, C. C. Lee, “Influences of temperature and stress on transmission characteristics of multilayer thin-film narrow bandpass filters,” Jpn. J. Appl. Phys. 40, 4087–4096 (2001).
[CrossRef]

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

2000 (1)

J. Han, J. Y. Kim, T. S. Kim, J. S. Kim, “Performance of Fabry–Perot microcavity structures with corrugated diaphragms,” Sens. Actuators A 79, 162–172 (2000).
[CrossRef]

1999 (1)

S. Sakaguchi, “Temperature dependence of transmission characteristics of multilayer film narrow bandpass filters,” Jpn. J. Appl. Phys. 38, 6362–6368 (1999).
[CrossRef]

1996 (1)

1995 (1)

Y. Kim, D. P. Neikirk, “Micromachined Fabry–Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7, 1471–1473 (1995).
[CrossRef]

1993 (1)

V. L. Spiering, S. Bouwstra, R. M. E. J. Spiering, “On-chip decoupling zone for package-stress reduction,” Sens. Actuators A 39, 149–156 (1993).
[CrossRef]

Aben, H.

H. Aben, C. Guillemet, Photoelasticity of Glass (Springer-Verlag, Berlin, 1993).
[CrossRef]

Abeysinghe, D. C.

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

Bouwstra, S.

V. L. Spiering, S. Bouwstra, R. M. E. J. Spiering, “On-chip decoupling zone for package-stress reduction,” Sens. Actuators A 39, 149–156 (1993).
[CrossRef]

Boyd, J. T.

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

Chen, T. C.

T. C. Chen, J. I. Kuo, W. L. Lee, C. C. Lee, “Influences of temperature and stress on transmission characteristics of multilayer thin-film narrow bandpass filters,” Jpn. J. Appl. Phys. 40, 4087–4096 (2001).
[CrossRef]

Cushing, D.

Dasgupta, S.

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

Gotzelmann, R.

Guillemet, C.

H. Aben, C. Guillemet, Photoelasticity of Glass (Springer-Verlag, Berlin, 1993).
[CrossRef]

Guo, D. G.

W. J. Wang, R. M. Lin, D. G. Guo, “Study of single deeply corrugated diaphragm for high sensitivity microphones,” J. Micromech. Microeng. 13, 184–189 (2003).
[CrossRef]

W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel non-planar diaphragm,” Microelectron. Eng. 70, 102–108 (2003).
[CrossRef]

Han, J.

J. Han, J. Y. Kim, T. S. Kim, J. S. Kim, “Performance of Fabry–Perot microcavity structures with corrugated diaphragms,” Sens. Actuators A 79, 162–172 (2000).
[CrossRef]

Jackson, H. E.

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

Kim, J. S.

J. Han, J. Y. Kim, T. S. Kim, J. S. Kim, “Performance of Fabry–Perot microcavity structures with corrugated diaphragms,” Sens. Actuators A 79, 162–172 (2000).
[CrossRef]

Kim, J. Y.

J. Han, J. Y. Kim, T. S. Kim, J. S. Kim, “Performance of Fabry–Perot microcavity structures with corrugated diaphragms,” Sens. Actuators A 79, 162–172 (2000).
[CrossRef]

Kim, T. S.

J. Han, J. Y. Kim, T. S. Kim, J. S. Kim, “Performance of Fabry–Perot microcavity structures with corrugated diaphragms,” Sens. Actuators A 79, 162–172 (2000).
[CrossRef]

Kim, Y.

Y. Kim, D. P. Neikirk, “Micromachined Fabry–Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7, 1471–1473 (1995).
[CrossRef]

Kuo, J. I.

T. C. Chen, J. I. Kuo, W. L. Lee, C. C. Lee, “Influences of temperature and stress on transmission characteristics of multilayer thin-film narrow bandpass filters,” Jpn. J. Appl. Phys. 40, 4087–4096 (2001).
[CrossRef]

Lee, C. C.

T. C. Chen, J. I. Kuo, W. L. Lee, C. C. Lee, “Influences of temperature and stress on transmission characteristics of multilayer thin-film narrow bandpass filters,” Jpn. J. Appl. Phys. 40, 4087–4096 (2001).
[CrossRef]

Lee, W. L.

T. C. Chen, J. I. Kuo, W. L. Lee, C. C. Lee, “Influences of temperature and stress on transmission characteristics of multilayer thin-film narrow bandpass filters,” Jpn. J. Appl. Phys. 40, 4087–4096 (2001).
[CrossRef]

Lin, R. M.

W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel non-planar diaphragm,” Microelectron. Eng. 70, 102–108 (2003).
[CrossRef]

W. J. Wang, R. M. Lin, D. G. Guo, “Study of single deeply corrugated diaphragm for high sensitivity microphones,” J. Micromech. Microeng. 13, 184–189 (2003).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, Bristol, UK, 2001).
[CrossRef]

Matl, K.

Neikirk, D. P.

Y. Kim, D. P. Neikirk, “Micromachined Fabry–Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7, 1471–1473 (1995).
[CrossRef]

Niordson, F. I.

F. I. Niordson, Shell Theory (North-Holland, Amsterdam, 1985).

Ren, Y.

W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel non-planar diaphragm,” Microelectron. Eng. 70, 102–108 (2003).
[CrossRef]

Sakaguchi, S.

S. Sakaguchi, “Temperature dependence of transmission characteristics of multilayer film narrow bandpass filters,” Jpn. J. Appl. Phys. 38, 6362–6368 (1999).
[CrossRef]

Spiering, R. M. E. J.

V. L. Spiering, S. Bouwstra, R. M. E. J. Spiering, “On-chip decoupling zone for package-stress reduction,” Sens. Actuators A 39, 149–156 (1993).
[CrossRef]

Spiering, V. L.

V. L. Spiering, S. Bouwstra, R. M. E. J. Spiering, “On-chip decoupling zone for package-stress reduction,” Sens. Actuators A 39, 149–156 (1993).
[CrossRef]

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

Sun, T. T.

W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel non-planar diaphragm,” Microelectron. Eng. 70, 102–108 (2003).
[CrossRef]

Wang, W. J.

W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel non-planar diaphragm,” Microelectron. Eng. 70, 102–108 (2003).
[CrossRef]

W. J. Wang, R. M. Lin, D. G. Guo, “Study of single deeply corrugated diaphragm for high sensitivity microphones,” J. Micromech. Microeng. 13, 184–189 (2003).
[CrossRef]

Zoller, A.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (2)

Y. Kim, D. P. Neikirk, “Micromachined Fabry–Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7, 1471–1473 (1995).
[CrossRef]

D. C. Abeysinghe, S. Dasgupta, J. T. Boyd, H. E. Jackson, “A novel MEMS pressure sensor fabricated on an optical fiber,” IEEE Photon. Technol. Lett. 13, 993–995 (2001).
[CrossRef]

J. Micromech. Microeng. (1)

W. J. Wang, R. M. Lin, D. G. Guo, “Study of single deeply corrugated diaphragm for high sensitivity microphones,” J. Micromech. Microeng. 13, 184–189 (2003).
[CrossRef]

Jpn. J. Appl. Phys. (2)

S. Sakaguchi, “Temperature dependence of transmission characteristics of multilayer film narrow bandpass filters,” Jpn. J. Appl. Phys. 38, 6362–6368 (1999).
[CrossRef]

T. C. Chen, J. I. Kuo, W. L. Lee, C. C. Lee, “Influences of temperature and stress on transmission characteristics of multilayer thin-film narrow bandpass filters,” Jpn. J. Appl. Phys. 40, 4087–4096 (2001).
[CrossRef]

Microelectron. Eng. (1)

W. J. Wang, R. M. Lin, T. T. Sun, D. G. Guo, Y. Ren, “Performance-enhanced Fabry–Perot microcavity structure with a novel non-planar diaphragm,” Microelectron. Eng. 70, 102–108 (2003).
[CrossRef]

Sens. Actuators A (2)

J. Han, J. Y. Kim, T. S. Kim, J. S. Kim, “Performance of Fabry–Perot microcavity structures with corrugated diaphragms,” Sens. Actuators A 79, 162–172 (2000).
[CrossRef]

V. L. Spiering, S. Bouwstra, R. M. E. J. Spiering, “On-chip decoupling zone for package-stress reduction,” Sens. Actuators A 39, 149–156 (1993).
[CrossRef]

Other (5)

F. I. Niordson, Shell Theory (North-Holland, Amsterdam, 1985).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

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

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, Bristol, UK, 2001).
[CrossRef]

H. Aben, C. Guillemet, Photoelasticity of Glass (Springer-Verlag, Berlin, 1993).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Schematic view of the proposed Fabry–Perot pressure sensor with a conventional flat diaphragm.

Fig. 2
Fig. 2

Interaction among temperature, stress, and optical behavior.

Fig. 3
Fig. 3

Thermal cross sensitivity of a FP microcavity pressure sensor with a conventional flat diaphragm with clamped edges under external loads of 30 psi.

Fig. 4
Fig. 4

Definition of the geometry and boundary conditions of the proposed SDCD.

Fig. 5
Fig. 5

Thermal stress-reduction factor of the proposed SDCD as a function of corrugation depth.

Fig. 6
Fig. 6

Thermal cross sensitivity of a FP microcavity pressure sensor with a SDCD under external loads of 30 psi.

Fig. 7
Fig. 7

Schematic view of the proposed FP microcavity pressure sensor. Polysi, polysilicon.

Fig. 8
Fig. 8

Measurement setup of the proposed FP microcavity pressure sensor.

Fig. 9
Fig. 9

Simulated and measured transmittances as a function of (a) wavelength and (b) applied pressure at room temperature (λ = 1310 nm).

Fig. 10
Fig. 10

Simulated (Simu) and measured (Meas) transmittances as a function of ambient temperatures (λ = 1310 nm) at different pressures.

Equations (30)

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R = ( η 0 B - C η 0 B + C ) ( η 0 B - C η 0 B + C ) * ,
T = 4 η 0 Re ( η f ) ( η 0 B + C ) ( η 0 B + C ) * ,
A = 4 η 0 Re ( BC * - η f ) ( η 0 B + C ) ( η 0 B + C ) * ,
[ B C ] = M [ 1 η f ] ,
M = M q M q - 1 M 2 M 1 ,
M i = [ cos ( k 0 n i d i ) ( j / η i ) sin ( k 0 n i d i ) j η i sin ( k 0 n i d i ) cos ( k 0 n i d i ) ] ,
σ x = σ y 0 ,             σ z = 0 ,
ɛ x = ɛ y = [ σ x - ν ( σ y + σ z ) ] / E = ( 1 - ν ) σ x / E = σ x / E 0 ,
ɛ z = [ σ z - ν ( σ x + σ y ) ] E = - 2 ν σ x / E .
α i Δ T + ɛ x i = α s Δ T - ɛ x s ,
σ x s d s = i = 1 5 σ x i d i = σ 1 d 1 + σ 2 d 2 ,
σ 1 = E s 0 ( α s - α 1 ) d s - E 2 0 ( α 1 - α 2 ) d 2 d 1 + E 2 0 / E 1 0 d 2 + ( E s 0 / E 1 0 E 1 0 ) Δ T ,
σ 2 = E 2 0 ( α s - α 2 ) d s - E 1 0 ( α 1 - α 2 ) d 1 E 1 0 / E 2 0 d 1 + d 2 + ( E s 0 / E 2 0 ) d s Δ T ,
σ 1 = E 1 0 ( α s - α 1 ) Δ T ,
σ 2 = E 2 0 ( α s - α 2 ) Δ T .
σ a = i ( σ i d i ) / i d i ,
Δ n = ( n T ) σ Δ T + ( n σ ) T Δ σ ,
Δ d = ( d T ) σ Δ T + ( d σ ) T Δ σ ,
u ( r ) = D τ cos α E d [ A 1 ( 2 ν bei 2 x - x bei 2 x ) - A 2 ( 2 ν ber 2 x - x ber 2 x ) + B 1 ( 2 ν kei 2 x - x kei 2 x ) - B 2 ( 2 ν ker 2 x - x ker 2 x ) ] ,
F ( r ) = - 16 D τ x 2 cos α ( A 1 bei 2 x - A 2 ber 2 x + B 1 kei 2 x - B 2 ker 2 x ) ,
Ψ ( r ) = A 1 ber 2 x + A 2 bei 2 x + B 1 ker 2 x + B 2 kei 2 x ,
M ( r ) = 4 D τ t g α x 2 [ A 1 ( 2 ν ber 2 x + x ber 2 x ) + A 2 ( 2 ν bei 2 x + x bei 2 x ) + B 1 ( 2 ν ker 2 x + x ker 2 x ) + B 2 ( 2 ν kei 2 x + x kei 2 x ) ] ,
τ = [ 3 ( 1 - ν 2 ) ] 1 / 2 d ,             x = ( 8 τ r tan α cos α ) 1 / 2 , D = E d 2 12 ( 1 - ν 2 ) .
ber 2 x - ber x - ( 1 2 π x ) 1 / 2 cos ( x 2 - π 8 ) exp ( x 2 ) ,
bei 2 x - bei x - ( 1 2 π x ) 1 / 2 sin ( x 2 - π 8 ) exp ( x 2 ) ,
ker 2 x - ker x - ( π 2 x ) 1 / 2 cos ( x 2 + π 8 ) exp ( - x 2 ) ,
kei 2 x - kei x ( π 2 x ) 1 / 2 sin ( x 2 + π 8 ) exp ( - x 2 ) .
F out F in M out M in C ( a b ) 5 / 2 exp [ F ( H ) ] = C ( 1 1 + H / atg α ) 5 / 2 exp [ K ( H ) ] ,
K ( H ) = x out - x in = 2 ( a sin α ) 1 / 2 [ 3 * ( 1 - ν 2 ) ] 1 / 4 [ ( 1 + H / atg α ) 1 / 2 - 1 ] cos α
σ out σ bottom ( 1 1 + H / arg α ) 5 / 2 exp [ K ( H ) ] ,

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