Abstract

In recent years, internal laser probing techniques that exploit the electro-optical and the thermo-optical effects have been introduced. Space-resolved and time-resolved measurements of charge-carrier and temperature distributions in the interior of semiconductor samples have thus become possible. For a profound analysis and the optimization of these measurement techniques, a physically rigorous model for simulating the entire measurement process is presented. The model includes the electrothermal device simulation of the sample’s operating condition, the calculation of the resulting refractive-index modulations, the simulation of wave propagation through the device under test, the imaging lenses and aperture holes, and the simulation of the detector response. As an essential part of this model, a numerically efficient algorithm for simulating wave propagation in large computational domains has been developed. The decisive step is introduction of a suitably chosen set of computational variables that allows a significantly coarser discretization width without loss of accuracy.

© 2003 Optical Society of America

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References

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  34. T. G. Moore, J. G. Blaschak, A. Taflove, G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Antennas Propag. 36, 1797–1812 (1988).
    [CrossRef]
  35. E Hecht, A Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).
  36. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  37. G. Cocorullo, F. G. D. Corte, M. Iodice, I. Rendina, P. M. Sarro, “A temperature all-silicon micro-sensor based on the thermo-optic effect,” IEEE Trans. Electron Devices 44, 766–774 (1997).
    [CrossRef]
  38. G. Cocorullo, F. G. D. Corte, I. Rendina, P. M. Sarro, “Thermo-optic effect exploitation in silicon microstructures,” Sens. Actuators A 71, 19–26 (1998).
    [CrossRef]
  39. T. Liu, G. F. Fernando, Z. Y. Zhang, K. T. V. Grattan, “Simultaneous strain and temperature measurements in composites using extrinsic Fabry–Perot interferometric and intrinsic rare-earth doped fiber sensors,” Sens. Actuators A 80, 208–215 (2000).
    [CrossRef]
  40. R Thalhammer, F Hille, P Scheubert, G Wachutka, “Physically rigorous modeling of sensing techniques exploiting the thermo-optical and electro-optical effect,” in Proceedings of International Conference on Modeling of Microsystems, Applied Computational Research Society, ed. (Computational Publications, Cambridge, Mass., 1999), pp. 683–686.

2003 (1)

2000 (1)

T. Liu, G. F. Fernando, Z. Y. Zhang, K. T. V. Grattan, “Simultaneous strain and temperature measurements in composites using extrinsic Fabry–Perot interferometric and intrinsic rare-earth doped fiber sensors,” Sens. Actuators A 80, 208–215 (2000).
[CrossRef]

1998 (1)

G. Cocorullo, F. G. D. Corte, I. Rendina, P. M. Sarro, “Thermo-optic effect exploitation in silicon microstructures,” Sens. Actuators A 71, 19–26 (1998).
[CrossRef]

1997 (2)

G. Cocorullo, F. G. D. Corte, M. Iodice, I. Rendina, P. M. Sarro, “A temperature all-silicon micro-sensor based on the thermo-optic effect,” IEEE Trans. Electron Devices 44, 766–774 (1997).
[CrossRef]

H. Kirchauer, S. Selberherr, “Rigorous three-dimensional photoresist exposure and development simula-tion over nonplanar topography,” IEEE Trans. Comput.-Aided Design 16, 1431–1438 (1997).
[CrossRef]

1996 (2)

N. Seliger, P. Habaš, E. Gornik, “A study of backside laser-probe signals in MOSFETs,” Microelectron. Eng. 31, 87–94 (1996).
[CrossRef]

G. Deboy, G. Sölkner, E. Wolfgang, W. Claeys, “Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection,” Microelectron. Eng. 31, 299–307 (1996).
[CrossRef]

1992 (1)

R. Z. Yahel, I. Last, “Numerical simulation of laser beam propagation in three-dimensional random media: beam splitting and patch formation,” Waves Random Media 2, 81–98 (1992).
[CrossRef]

1991 (1)

1990 (2)

G. Wachutka, “Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling,” IEEE Trans. Comput. Aided Des. 9, 1141–1149 (1990).
[CrossRef]

H. Bleichner, E. Nordlander, M. Rosling, S. Berg, “A time-resolved optical system for spatial characterization of the carrier distribution in a gate-turn-off thyristor (GTO),” IEEE Trans. Instrum. Meas. 39, 473–478 (1990).
[CrossRef]

1988 (1)

T. G. Moore, J. G. Blaschak, A. Taflove, G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Antennas Propag. 36, 1797–1812 (1988).
[CrossRef]

1987 (1)

P. E. Lagasse, R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems: a review,” Radio Sci. 22, 1225–1233 (1987).
[CrossRef]

1986 (1)

D. Fournier, C. Boccara, A. Skumanich, N. M. Amer, “Photothermal investigation of transport in semiconductors: theory and experiment,” J. Appl. Phys. 59, 787–795 (1986).
[CrossRef]

1981 (1)

1978 (2)

R. W. Cooper, D. H. Paxman, “Measurement of charge carrier behavior in pin diodes using a laser technique,” Solid State Electron. 21, 865–869 (1978).
[CrossRef]

M. D. Feit, J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
[CrossRef] [PubMed]

1966 (2)

C. B. Burckhardt, “Diffraction of a plane wave at a sinusoidally stratified dielectric grating,” J. Opt. Soc. Am. 56, 1502–1509 (1966).
[CrossRef]

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

1956 (1)

N. J. Harrick, “Use of infrared absorption to determine carrier distribution in germanium and surface recombination velocity,” Phys. Rev. 101, 491 (1956).
[CrossRef]

1953 (1)

H. B. Briggs, R. C. Fletcher, “Absorption of infrared light by free carriers in germanium,” Phys. Rev. 91, 1342–1346 (1953).
[CrossRef]

Amer, N. M.

D. Fournier, C. Boccara, A. Skumanich, N. M. Amer, “Photothermal investigation of transport in semiconductors: theory and experiment,” J. Appl. Phys. 59, 787–795 (1986).
[CrossRef]

Baets, R.

P. E. Lagasse, R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems: a review,” Radio Sci. 22, 1225–1233 (1987).
[CrossRef]

Berg, S.

H. Bleichner, E. Nordlander, M. Rosling, S. Berg, “A time-resolved optical system for spatial characterization of the carrier distribution in a gate-turn-off thyristor (GTO),” IEEE Trans. Instrum. Meas. 39, 473–478 (1990).
[CrossRef]

Blaschak, J. G.

T. G. Moore, J. G. Blaschak, A. Taflove, G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Antennas Propag. 36, 1797–1812 (1988).
[CrossRef]

Bleichner, H.

H. Bleichner, E. Nordlander, M. Rosling, S. Berg, “A time-resolved optical system for spatial characterization of the carrier distribution in a gate-turn-off thyristor (GTO),” IEEE Trans. Instrum. Meas. 39, 473–478 (1990).
[CrossRef]

Boccara, C.

D. Fournier, C. Boccara, A. Skumanich, N. M. Amer, “Photothermal investigation of transport in semiconductors: theory and experiment,” J. Appl. Phys. 59, 787–795 (1986).
[CrossRef]

Briggs, H. B.

H. B. Briggs, R. C. Fletcher, “Absorption of infrared light by free carriers in germanium,” Phys. Rev. 91, 1342–1346 (1953).
[CrossRef]

Burckhardt, C. B.

Claeys, W.

G. Deboy, G. Sölkner, E. Wolfgang, W. Claeys, “Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection,” Microelectron. Eng. 31, 299–307 (1996).
[CrossRef]

Cocorullo, G.

G. Cocorullo, F. G. D. Corte, I. Rendina, P. M. Sarro, “Thermo-optic effect exploitation in silicon microstructures,” Sens. Actuators A 71, 19–26 (1998).
[CrossRef]

G. Cocorullo, F. G. D. Corte, M. Iodice, I. Rendina, P. M. Sarro, “A temperature all-silicon micro-sensor based on the thermo-optic effect,” IEEE Trans. Electron Devices 44, 766–774 (1997).
[CrossRef]

Cooper, R. W.

R. W. Cooper, D. H. Paxman, “Measurement of charge carrier behavior in pin diodes using a laser technique,” Solid State Electron. 21, 865–869 (1978).
[CrossRef]

Corte, F. G. D.

G. Cocorullo, F. G. D. Corte, I. Rendina, P. M. Sarro, “Thermo-optic effect exploitation in silicon microstructures,” Sens. Actuators A 71, 19–26 (1998).
[CrossRef]

G. Cocorullo, F. G. D. Corte, M. Iodice, I. Rendina, P. M. Sarro, “A temperature all-silicon micro-sensor based on the thermo-optic effect,” IEEE Trans. Electron Devices 44, 766–774 (1997).
[CrossRef]

Deboy, G

G Deboy, “Charakterisierung von Leistungshalbleitern durch Interne Laserdeflektion,” Ph.D. thesis (Technische Universität München, Munich, Germany, 1996).

Deboy, G.

G. Deboy, G. Sölkner, E. Wolfgang, W. Claeys, “Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection,” Microelectron. Eng. 31, 299–307 (1996).
[CrossRef]

Escoffier, R

R Escoffier, U Krumbein, E Lyumkis, B Polsky, A Schenk, B Schmithüsen, C. Steiner, W. Fichtner, DESSIS 4.0 Manual (ISE Integrated Systems Engineering, Zurich, Switzerland, 1996).

Feit, M. D.

Fernando, G. F.

T. Liu, G. F. Fernando, Z. Y. Zhang, K. T. V. Grattan, “Simultaneous strain and temperature measurements in composites using extrinsic Fabry–Perot interferometric and intrinsic rare-earth doped fiber sensors,” Sens. Actuators A 80, 208–215 (2000).
[CrossRef]

Fichtner, W.

R Escoffier, U Krumbein, E Lyumkis, B Polsky, A Schenk, B Schmithüsen, C. Steiner, W. Fichtner, DESSIS 4.0 Manual (ISE Integrated Systems Engineering, Zurich, Switzerland, 1996).

Fleck, J. A.

Fletcher, R. C.

H. B. Briggs, R. C. Fletcher, “Absorption of infrared light by free carriers in germanium,” Phys. Rev. 91, 1342–1346 (1953).
[CrossRef]

Fournier, D.

D. Fournier, C. Boccara, A. Skumanich, N. M. Amer, “Photothermal investigation of transport in semiconductors: theory and experiment,” J. Appl. Phys. 59, 787–795 (1986).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gornik, E.

N. Seliger, P. Habaš, E. Gornik, “A study of backside laser-probe signals in MOSFETs,” Microelectron. Eng. 31, 87–94 (1996).
[CrossRef]

N Seliger, P Habaš, E. Gornik, “Time-domain characterization of lattice heating in power VDMOSFETs by means of an interferometric laserprobe technique,” in Proceedings of European Solid State Device Research Conference, G. Baccarani, M. Rudan, eds. (Editions Frontières, Gif-sur-Yvette, France, 1996), pp. 847–850.

Görtz, W

W Görtz, “Ein Beitrag zur Bestimmung des Ladungsträgerverhaltens in psn-Dioden im Fall starker Injektion unter Verwendung der Absorptions-Messmethode,” Ph.D. thesis (Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany, 1984).

Grattan, K. T. V.

T. Liu, G. F. Fernando, Z. Y. Zhang, K. T. V. Grattan, “Simultaneous strain and temperature measurements in composites using extrinsic Fabry–Perot interferometric and intrinsic rare-earth doped fiber sensors,” Sens. Actuators A 80, 208–215 (2000).
[CrossRef]

Habaš, P

N Seliger, P Habaš, E. Gornik, “Time-domain characterization of lattice heating in power VDMOSFETs by means of an interferometric laserprobe technique,” in Proceedings of European Solid State Device Research Conference, G. Baccarani, M. Rudan, eds. (Editions Frontières, Gif-sur-Yvette, France, 1996), pp. 847–850.

Habaš, P.

N. Seliger, P. Habaš, E. Gornik, “A study of backside laser-probe signals in MOSFETs,” Microelectron. Eng. 31, 87–94 (1996).
[CrossRef]

Hafner, C

C Hafner, “Beiträge zur Berechnung der Ausbreitung elektromagnetischer Wellen in zylindrischen Strukturen mit Hilfe des ‘Point Matching Verfahrens,’ ” Ph.D. thesis (Eidgenössische Technische Hochschule Zürich, Zurich, Switzerland, 1980).

C Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Norwood, Mass., 1990).

Harrick, N. J.

N. J. Harrick, “Use of infrared absorption to determine carrier distribution in germanium and surface recombination velocity,” Phys. Rev. 101, 491 (1956).
[CrossRef]

Hecht, E

E Hecht, A Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).

Hille, F

R Thalhammer, F Hille, P Scheubert, G Wachutka, “Physically rigorous modeling of sensing techniques exploiting the thermo-optical and electro-optical effect,” in Proceedings of International Conference on Modeling of Microsystems, Applied Computational Research Society, ed. (Computational Publications, Cambridge, Mass., 1999), pp. 683–686.

Houston, D. E.

D. E. Houston, S Krishna, E. D. Wolley, “Study of charge dynamics in high speed power devices using free carrier absorption measurement,” in Technical Digest of International Electronic Devices Meeting (Institute of Electrical and Electronics Engineers, New York, 1976), pp. 504–507.

Iodice, M.

G. Cocorullo, F. G. D. Corte, M. Iodice, I. Rendina, P. M. Sarro, “A temperature all-silicon micro-sensor based on the thermo-optic effect,” IEEE Trans. Electron Devices 44, 766–774 (1997).
[CrossRef]

Kirchauer, H.

H. Kirchauer, S. Selberherr, “Rigorous three-dimensional photoresist exposure and development simula-tion over nonplanar topography,” IEEE Trans. Comput.-Aided Design 16, 1431–1438 (1997).
[CrossRef]

Koch, T. B.

T. B. Koch, “Computation of wave propagation in integrated optical devices,” Ph.D. thesis (University College, London, 1989).

Körner, T. O.

T. O. Körner, Rigorous Simulation of Light Propagation in Semiconductor Devices, Vol. 81 of Series in Microelectronics (Hartung-Gorre, Konstanz, Germany, 1999).

Kriegsmann, G. A.

T. G. Moore, J. G. Blaschak, A. Taflove, G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Antennas Propag. 36, 1797–1812 (1988).
[CrossRef]

Krishna, S

D. E. Houston, S Krishna, E. D. Wolley, “Study of charge dynamics in high speed power devices using free carrier absorption measurement,” in Technical Digest of International Electronic Devices Meeting (Institute of Electrical and Electronics Engineers, New York, 1976), pp. 504–507.

Krumbein, U

R Escoffier, U Krumbein, E Lyumkis, B Polsky, A Schenk, B Schmithüsen, C. Steiner, W. Fichtner, DESSIS 4.0 Manual (ISE Integrated Systems Engineering, Zurich, Switzerland, 1996).

Lagasse, P. E.

P. E. Lagasse, R. Baets, “Application of propagating beam methods to electromagnetic and acoustic wave propagation problems: a review,” Radio Sci. 22, 1225–1233 (1987).
[CrossRef]

J. V. Roey, J. van der Donk, P. E. Lagasse, “Beam-propagation method: analysis and assessment,” J. Opt. Soc. Am. 71, 803–810 (1981).
[CrossRef]

Last, I.

R. Z. Yahel, I. Last, “Numerical simulation of laser beam propagation in three-dimensional random media: beam splitting and patch formation,” Waves Random Media 2, 81–98 (1992).
[CrossRef]

Liu, T.

T. Liu, G. F. Fernando, Z. Y. Zhang, K. T. V. Grattan, “Simultaneous strain and temperature measurements in composites using extrinsic Fabry–Perot interferometric and intrinsic rare-earth doped fiber sensors,” Sens. Actuators A 80, 208–215 (2000).
[CrossRef]

Lyumkis, E

R Escoffier, U Krumbein, E Lyumkis, B Polsky, A Schenk, B Schmithüsen, C. Steiner, W. Fichtner, DESSIS 4.0 Manual (ISE Integrated Systems Engineering, Zurich, Switzerland, 1996).

Moore, T. G.

T. G. Moore, J. G. Blaschak, A. Taflove, G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Antennas Propag. 36, 1797–1812 (1988).
[CrossRef]

Niederhoff, M

M Niederhoff, “Feldberechnung in Hochleistungslaserdioden,” Ph.D. thesis (Technische Universität München, Munich, Germany, 1996).

Nordlander, E.

H. Bleichner, E. Nordlander, M. Rosling, S. Berg, “A time-resolved optical system for spatial characterization of the carrier distribution in a gate-turn-off thyristor (GTO),” IEEE Trans. Instrum. Meas. 39, 473–478 (1990).
[CrossRef]

Paxman, D. H.

R. W. Cooper, D. H. Paxman, “Measurement of charge carrier behavior in pin diodes using a laser technique,” Solid State Electron. 21, 865–869 (1978).
[CrossRef]

Petit, R

R Petit, Electromagnetic Theory of Gratings (Springer, Berlin, 1980).

Polsky, B

R Escoffier, U Krumbein, E Lyumkis, B Polsky, A Schenk, B Schmithüsen, C. Steiner, W. Fichtner, DESSIS 4.0 Manual (ISE Integrated Systems Engineering, Zurich, Switzerland, 1996).

Rendina, I.

G. Cocorullo, F. G. D. Corte, I. Rendina, P. M. Sarro, “Thermo-optic effect exploitation in silicon microstructures,” Sens. Actuators A 71, 19–26 (1998).
[CrossRef]

G. Cocorullo, F. G. D. Corte, M. Iodice, I. Rendina, P. M. Sarro, “A temperature all-silicon micro-sensor based on the thermo-optic effect,” IEEE Trans. Electron Devices 44, 766–774 (1997).
[CrossRef]

Roey, J. V.

Rosling, M.

H. Bleichner, E. Nordlander, M. Rosling, S. Berg, “A time-resolved optical system for spatial characterization of the carrier distribution in a gate-turn-off thyristor (GTO),” IEEE Trans. Instrum. Meas. 39, 473–478 (1990).
[CrossRef]

Sarro, P. M.

G. Cocorullo, F. G. D. Corte, I. Rendina, P. M. Sarro, “Thermo-optic effect exploitation in silicon microstructures,” Sens. Actuators A 71, 19–26 (1998).
[CrossRef]

G. Cocorullo, F. G. D. Corte, M. Iodice, I. Rendina, P. M. Sarro, “A temperature all-silicon micro-sensor based on the thermo-optic effect,” IEEE Trans. Electron Devices 44, 766–774 (1997).
[CrossRef]

Schenk, A

R Escoffier, U Krumbein, E Lyumkis, B Polsky, A Schenk, B Schmithüsen, C. Steiner, W. Fichtner, DESSIS 4.0 Manual (ISE Integrated Systems Engineering, Zurich, Switzerland, 1996).

A Schenk, Advanced Physical Models for Silicon Device Simulation (Springer, Vienna, 1998).

Scheubert, P

R Thalhammer, F Hille, P Scheubert, G Wachutka, “Physically rigorous modeling of sensing techniques exploiting the thermo-optical and electro-optical effect,” in Proceedings of International Conference on Modeling of Microsystems, Applied Computational Research Society, ed. (Computational Publications, Cambridge, Mass., 1999), pp. 683–686.

Schierwater, G

G Schierwater, “Untersuchung der optischen Absorption an freien Ladungsträgern und der Rekombinationsstrahl-ung am Elektron-Loch-Plasma von pin-Dioden,” Ph.D. thesis (Technische Universität Berlin, Berlin, 1975).

Schmithüsen, B

R Escoffier, U Krumbein, E Lyumkis, B Polsky, A Schenk, B Schmithüsen, C. Steiner, W. Fichtner, DESSIS 4.0 Manual (ISE Integrated Systems Engineering, Zurich, Switzerland, 1996).

Selberherr, S.

H. Kirchauer, S. Selberherr, “Rigorous three-dimensional photoresist exposure and development simula-tion over nonplanar topography,” IEEE Trans. Comput.-Aided Design 16, 1431–1438 (1997).
[CrossRef]

Seliger, N

N Seliger, “Characterization of semiconductor devices by laser interferometry,” Ph.D. thesis (Vienna University of Technology, Vienna, 1998).

N Seliger, P Habaš, E. Gornik, “Time-domain characterization of lattice heating in power VDMOSFETs by means of an interferometric laserprobe technique,” in Proceedings of European Solid State Device Research Conference, G. Baccarani, M. Rudan, eds. (Editions Frontières, Gif-sur-Yvette, France, 1996), pp. 847–850.

Seliger, N.

N. Seliger, P. Habaš, E. Gornik, “A study of backside laser-probe signals in MOSFETs,” Microelectron. Eng. 31, 87–94 (1996).
[CrossRef]

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G. Deboy, G. Sölkner, E. Wolfgang, W. Claeys, “Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection,” Microelectron. Eng. 31, 299–307 (1996).
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R Thalhammer, F Hille, P Scheubert, G Wachutka, “Physically rigorous modeling of sensing techniques exploiting the thermo-optical and electro-optical effect,” in Proceedings of International Conference on Modeling of Microsystems, Applied Computational Research Society, ed. (Computational Publications, Cambridge, Mass., 1999), pp. 683–686.

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J. W. Thomas, Numerical Partial Differential Equations:Finite Difference Methods, Vol. 22 of Texts in Applied Mathematics (Springer, Berlin, 1995).

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Wachutka, G

R Thalhammer, F Hille, P Scheubert, G Wachutka, “Physically rigorous modeling of sensing techniques exploiting the thermo-optical and electro-optical effect,” in Proceedings of International Conference on Modeling of Microsystems, Applied Computational Research Society, ed. (Computational Publications, Cambridge, Mass., 1999), pp. 683–686.

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G. Deboy, G. Sölkner, E. Wolfgang, W. Claeys, “Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection,” Microelectron. Eng. 31, 299–307 (1996).
[CrossRef]

Wolley, E. D.

D. E. Houston, S Krishna, E. D. Wolley, “Study of charge dynamics in high speed power devices using free carrier absorption measurement,” in Technical Digest of International Electronic Devices Meeting (Institute of Electrical and Electronics Engineers, New York, 1976), pp. 504–507.

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R. Z. Yahel, I. Last, “Numerical simulation of laser beam propagation in three-dimensional random media: beam splitting and patch formation,” Waves Random Media 2, 81–98 (1992).
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K. S. Yee, “Numerical simulation of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
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M. S. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 149–167 (1988).
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T. Liu, G. F. Fernando, Z. Y. Zhang, K. T. V. Grattan, “Simultaneous strain and temperature measurements in composites using extrinsic Fabry–Perot interferometric and intrinsic rare-earth doped fiber sensors,” Sens. Actuators A 80, 208–215 (2000).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (2)

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

T. G. Moore, J. G. Blaschak, A. Taflove, G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Antennas Propag. 36, 1797–1812 (1988).
[CrossRef]

IEEE Trans. Comput. Aided Des. (1)

G. Wachutka, “Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling,” IEEE Trans. Comput. Aided Des. 9, 1141–1149 (1990).
[CrossRef]

IEEE Trans. Comput.-Aided Design (1)

H. Kirchauer, S. Selberherr, “Rigorous three-dimensional photoresist exposure and development simula-tion over nonplanar topography,” IEEE Trans. Comput.-Aided Design 16, 1431–1438 (1997).
[CrossRef]

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G. Cocorullo, F. G. D. Corte, M. Iodice, I. Rendina, P. M. Sarro, “A temperature all-silicon micro-sensor based on the thermo-optic effect,” IEEE Trans. Electron Devices 44, 766–774 (1997).
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H. Bleichner, E. Nordlander, M. Rosling, S. Berg, “A time-resolved optical system for spatial characterization of the carrier distribution in a gate-turn-off thyristor (GTO),” IEEE Trans. Instrum. Meas. 39, 473–478 (1990).
[CrossRef]

J. Appl. Phys. (1)

D. Fournier, C. Boccara, A. Skumanich, N. M. Amer, “Photothermal investigation of transport in semiconductors: theory and experiment,” J. Appl. Phys. 59, 787–795 (1986).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Microelectron. Eng. (2)

N. Seliger, P. Habaš, E. Gornik, “A study of backside laser-probe signals in MOSFETs,” Microelectron. Eng. 31, 87–94 (1996).
[CrossRef]

G. Deboy, G. Sölkner, E. Wolfgang, W. Claeys, “Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection,” Microelectron. Eng. 31, 299–307 (1996).
[CrossRef]

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G. Cocorullo, F. G. D. Corte, I. Rendina, P. M. Sarro, “Thermo-optic effect exploitation in silicon microstructures,” Sens. Actuators A 71, 19–26 (1998).
[CrossRef]

T. Liu, G. F. Fernando, Z. Y. Zhang, K. T. V. Grattan, “Simultaneous strain and temperature measurements in composites using extrinsic Fabry–Perot interferometric and intrinsic rare-earth doped fiber sensors,” Sens. Actuators A 80, 208–215 (2000).
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Other (19)

M Niederhoff, “Feldberechnung in Hochleistungslaserdioden,” Ph.D. thesis (Technische Universität München, Munich, Germany, 1996).

J. W. Thomas, Numerical Partial Differential Equations:Finite Difference Methods, Vol. 22 of Texts in Applied Mathematics (Springer, Berlin, 1995).

E Hecht, A Zajac, Optics (Addison-Wesley, Reading, Mass., 1974).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

R Petit, Electromagnetic Theory of Gratings (Springer, Berlin, 1980).

M. S. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 149–167 (1988).
[CrossRef]

W Görtz, “Ein Beitrag zur Bestimmung des Ladungsträgerverhaltens in psn-Dioden im Fall starker Injektion unter Verwendung der Absorptions-Messmethode,” Ph.D. thesis (Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany, 1984).

G Deboy, “Charakterisierung von Leistungshalbleitern durch Interne Laserdeflektion,” Ph.D. thesis (Technische Universität München, Munich, Germany, 1996).

N Seliger, P Habaš, E. Gornik, “Time-domain characterization of lattice heating in power VDMOSFETs by means of an interferometric laserprobe technique,” in Proceedings of European Solid State Device Research Conference, G. Baccarani, M. Rudan, eds. (Editions Frontières, Gif-sur-Yvette, France, 1996), pp. 847–850.

G Schierwater, “Untersuchung der optischen Absorption an freien Ladungsträgern und der Rekombinationsstrahl-ung am Elektron-Loch-Plasma von pin-Dioden,” Ph.D. thesis (Technische Universität Berlin, Berlin, 1975).

D. E. Houston, S Krishna, E. D. Wolley, “Study of charge dynamics in high speed power devices using free carrier absorption measurement,” in Technical Digest of International Electronic Devices Meeting (Institute of Electrical and Electronics Engineers, New York, 1976), pp. 504–507.

R Escoffier, U Krumbein, E Lyumkis, B Polsky, A Schenk, B Schmithüsen, C. Steiner, W. Fichtner, DESSIS 4.0 Manual (ISE Integrated Systems Engineering, Zurich, Switzerland, 1996).

A Schenk, Advanced Physical Models for Silicon Device Simulation (Springer, Vienna, 1998).

N Seliger, “Characterization of semiconductor devices by laser interferometry,” Ph.D. thesis (Vienna University of Technology, Vienna, 1998).

T. B. Koch, “Computation of wave propagation in integrated optical devices,” Ph.D. thesis (University College, London, 1989).

C Hafner, “Beiträge zur Berechnung der Ausbreitung elektromagnetischer Wellen in zylindrischen Strukturen mit Hilfe des ‘Point Matching Verfahrens,’ ” Ph.D. thesis (Eidgenössische Technische Hochschule Zürich, Zurich, Switzerland, 1980).

C Hafner, The Generalized Multipole Technique for Computational Electromagnetics (Artech House, Norwood, Mass., 1990).

T. O. Körner, Rigorous Simulation of Light Propagation in Semiconductor Devices, Vol. 81 of Series in Microelectronics (Hartung-Gorre, Konstanz, Germany, 1999).

R Thalhammer, F Hille, P Scheubert, G Wachutka, “Physically rigorous modeling of sensing techniques exploiting the thermo-optical and electro-optical effect,” in Proceedings of International Conference on Modeling of Microsystems, Applied Computational Research Society, ed. (Computational Publications, Cambridge, Mass., 1999), pp. 683–686.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for internal laser deflection measurements on power devices (e.g., an insulated gate bipolar transistor sample). Charge-carrier and temperature gradients originate a deflection of the laser beam, which is transformed into a parallel shift on the detector. The dashed curves indicate the shifted probing beam.

Fig. 2
Fig. 2

Modeling optical probing techniques. The solid arrows indicate the steps for simulating the measurement process on a structure subjected to a specific operating condition. A real experiment follows the dashed arrows.

Fig. 3
Fig. 3

Refraction of incident waves with given wave-vector component k x at an interface with dielectric constant l on the left and r on the right.

Fig. 4
Fig. 4

Modeling the image formation by optical elements, e.g., by a lens. On a sequence of parallel planes z = z k , k = 1 ,   2 , , the electric field E ( x ,   y ,   z k + 1 ) on each plane z = z k + 1 is calculated from the field E ( x ,   y ,   z k ) on plane z = z k .

Fig. 5
Fig. 5

Intensity distribution along a cutline across the detector. The intervals [ x 1 ,   x 2 ] and [ x 3 ,   x 4 ] correspond to the detector segments. The detected intensity is proportional to the shaded areas.

Equations (46)

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n t - 1 q   J n = - R , p t + 1 q   J p = - R ,
J n = - q μ n n ( Φ n + P n T ) ,
J p = - q μ p p ( Φ p + P p T ) .
( Ψ ) = q ( n - p + N A - - N D + ) .
c tot   T t - ( κ T ) = H ,
n ω ( n ,   p ,   T ) = n ω , 0 + n ω n p , T Δ n + n ω p n , T Δ p + n ω T n , p Δ T n = p n ω , 0 + n ω C T Δ n + n ω T n , p Δ T ,
α ( n ,   p ,   T ) n = p α 0 + α C T Δ n + α T n , p Δ T .
z   E y ( x ,   z ) = - i ω B x ( x ,   z ) ,
z   B x ( x ,   z ) = - i   ω c 2   R ( x ,   z ) E y ( x ,   z ) - i ω   2 x 2   E y ( x ,   z ) .
E F ( x ,   z )     1 2   exp ( - i κ z ) E y ( x ,   z ) - ω κ   B x ( x ,   z ) ,
E B ( x ,   z )     1 2   exp ( i κ z ) E y ( x ,   z ) + ω κ   B x ( x ,   z ) .
z   E F = i ω 2 2 c 2 κ   R E F + i 2 κ   2 x 2   E F - i κ 2   E F + i ω 2 2 c 2 κ   R   exp ( - 2 i κ z ) E B + i 2 κ   exp ( - 2 i κ z )   2 x 2   E B - i κ 2   exp ( - 2 i κ z ) E B ,
z   E B = - i ω 2 2 c 2 κ   R E B - i 2 κ   2 x 2   E B + i κ 2   E B - i ω 2 2 c 2 κ   R   exp ( 2 i κ z ) E F - i 2 κ   exp ( 2 i κ z )   2 x 2   E F + i κ 2   exp ( 2 i κ z ) E F .
M k , 2 U ( z k + 1 ) = M k , 1 U ( z k ) ,
U ( z k )     [ E F ( x 1 ,   z k ) ,   E B ( x 1 ,   z k ) , ,   E F ( x N x ,   z k ) ,   E B ( x N x ,   z k ) ] T .
U ( z k + 1 ) = P k U ( z k ) ,
P k = M k , 2 - 1 M k , 1 .
U ( z N z ) = P U ( z 1 ) , P = k = 1 N z - 1 P k .
E ˜ + l ( k x ,   0 ) E ˜ - l ( k x ,   0 ) = k z l + k z r 2 k z l k z l - k z r 2 k z l k z l - k z r 2 k z l k z l + k z r 2 k z l   E ˜ + s r ( k x ,   0 ) E ˜ - r ( k x ,   0 ) ,
E ˜ i ( k x ) = 1 2   1 + κ k z a exp ( i κ z 1 ) E ˜ F ( k x ,   z 1 ) + 1 2   1 - κ k z a exp ( - i κ z 1 ) E ˜ B ( k x ,   z 1 )
E ˜ r ( k x ) = 1 2   1 - κ k z a exp ( i κ z 1 ) E ˜ F ( k x ,   z 1 ) + 1 2   1 + κ k z a exp ( - i κ z 1 ) E ˜ B ( k x ,   z 1 ) .
[ B ˜ ± a , b ] i , 2 i     1 2   1 ± κ k z a , b ,
[ B ˜ ± a , b ] i , 2 i + 1     1 2   1 κ k z a , b for i = 1 , , N x   ,
[ B ˜ ± a , b ] i , j     0 otherwise
E ˜ i = B ˜ + a U ˜ ( z 1 ) , 0 = B ˜ - b U ˜ ( z N z ) .
E ˜ r = B ˜ - a U ˜ ( z 1 ) , E ˜ t = B ˜ + b U ˜ ( z N z ) .
1 k z a , b = 1 a , b k 0   1 - 1 2 a , b k 0 2   2 x 2 + O 4 x 4 .
E i = B + a U ( z 1 ) , 0 = B - b U ( z N z ) ,
B ± a , b = T B ˜ ± a , b T - 1 .
B + a B - b P U ( z 1 ) = E i 0
E r E t = B - a B + b P U ( z 1 ) .
E ( x ,   y ,   z k + 1 ) = Θ ( R 2 - x 2 - y 2 ) E ( x ,   y ,   z k ) ,
φ ( x ,   y ) = k 0 n L Δ 0 + k 0 2   f   ( x 2 + y 2 ) ,
E ( x ,   y ,   z k + 1 ) = exp ( ik 0 n L Δ 0 × ) exp i   k 0 2   f   ( x 2 + y 2 ) E ( x ,   y ,   z k ) .
E ( x ,   y ,   z ) = E ˜ ( k x ,   k y ) exp [ ik z ( k x ,   k y ) z ] × exp ( ik x x + ik y y ) d k x d k y .
E ˜ ( k x ,   k y ,   z k + 1 ) = exp [ i ( k 0 2 - k x 2 - k y 2 ) 1 / 2 ( z k + 1 - z k ) ] × E ˜ ( k x ,   k y ,   z k ) .
I 1 ( t ) = const   x 1 x 2 E D ( x ,   t ) 2 d x .
M ( t ) = I 1 ( t ) - I 2 ( t ) I 1 ( t ) + I 2 ( t ) , A ( t ) = I 1 ( t ) + I 2 ( t ) I 1 off + I 2 off - 1 .
A k ( x ) - i Δ z k 4 κ   x 2 B k ( x ) + K k x 2 C k ( x ) + K k * x 2 D k ( x ) + i Δ z k 4 κ   x 2   E F ( x ,   z k + 1 ) E B ( x ,   z k + 1 )
= A ˜ k ( x ) + i Δ z k 4 κ   x 2 B ˜ k ( x ) + K ˜ k x 2 C ˜ k ( x ) + K ˜ k * x 2 D ˜ k ( x ) - i Δ z k 4 κ   x 2   E F ( x ,   z k ) E B ( x ,   z k ) .
M k , j 1 u ( x j + 1 ,   z k + 1 ) + M k , j 2 u ( x j ,   z k + 1 )
+ M k , j 3 u ( x j - 1 ,   z k + 1 )
= M k , j 4 u ( x j + 1 ,   z k ) + M k , j 5 u ( x j ,   z k ) + M k , j 6 u ( x j - 1 ,   z k ) ,
u ( x j ,   z k ) = E F ( x j ,   z k ) E B ( x j ,   z k ) .
M 1 , k U ( z k + 1 ) = M 2 , k U ( z k ) ,
M 1 , k = M k , j - 1 3 M k , j - 1 2 M k , j - 1 1 M k , j 3 M k , j 2 M k , j 1 .

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