Abstract

In laser soldering, one has direct control over the incident laser pulse energy and duration but only indirect control over the temperature profile of the parts to be soldered. To understand the conversion of incident laser energy into a substrate temperature profile, two processes need to be understood: first, the optical absorption as a function of temperature and, second, the temperature distribution as a function of absorbed energy. The optical absorption aspect is addressed here. A set of total reflectivity measurements for real surfaces of interest is presented along with analytical calculations of the temperature dependence of the optical absorption for both specular and rough surfaces.

© 1989 Optical Society of America

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  1. The integrating sphere accessory is the DRTA-9A made by Lapshere, Inc. as an accessory for the Perkin-Elmer Lambda-9 UV-VIS-NIR spectrometer. The actual reflectivity measurements were made at Labsphere. This schematic is a simplified version of a drawing from a Labsphere, Inc. product brochure.
  2. The x-ray analyzer was calibrated by analyzing an NBS Standard Reference Material 1131, which is a 40:60 Sn:Pb standard. The analyzer gave a 38:62 composition and is thus regarded as accurate to ∼2%.
  3. The soldering bath was purchased from Technic, Inc. This is a fluoborate sulfonic acid type system with ∼0.02% occluded carbon deposits.
  4. E. Lish, Lasers Tackle Tough Soldering Problems (Electronic Packaging & Production, June1984), p. 154.
  5. The solder paste is manufactured by Kester Solder, part R-229D, vacuum dried at 80°C for 30 min.
  6. Kapton is a trademark of the Dupont Company. The measurement of the total reflectivity does not give information about the transmission properties of the film. It is assumed in table IV that the polyimide will be backed up with an opaque material so that the effective absorption may be obtained from the reflectivity by assuming that the sum of the absorption and reflectivity is unity.
  7. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).
  8. The undesirable effects of splattering may be reduced by spatially scanning the laser during the heating period.
  9. P. Drude, Ann. Phys. 39, 504 (1890).
  10. F. Bloch, Z. Phys. 52, 555 (1928).
  11. ℱ5(x)=∫0x[(z5ez)/(ez−1)2]dz, J. Ziman, Electrons and Phonons (Oxford U.P., London, 1979), p. 54.
  12. W. Rodgers, R. Powell, Tables of Transport Integrals, Natl. Bur. Stand. U.S. Circ.595 (1958).
  13. The Debye temperatures for Sn and Au are both ∼170 K, so that above room temperature T ≥ ϴD and ℱ5(x) converges to ℱ5 = ¼[(ϴD)/T]4.
  14. R. Klein Wassink, Soldering in Electronics (Electrochemical Publications, London, 1984), p. 105.
  15. C. Kent, “The Optical Constants of Liquid Alloys,” Phys. Rev. 14, 459–489 (1919).
    [CrossRef]
  16. J. Hodgson, “The Optical Properties of Liquid Germanium, Tin and Lead,” Philos. Mag. 6, 509–515 (1961).
    [CrossRef]
  17. E. Gruneisen, “Title,” Handb. Phys 13, 28–00 (1928).
  18. G. Kaye, T. Laby, Table of Physical and Chemical Constants (Longmans Green, London, 1966).
  19. Although the SnPb system as an alloy is not accurately described by the Bloch formula, the approximation of linear temperature dependence is used here for simplicity.
  20. A. Golovashkin, P. Motulevich, “Optical Properties of Tin at Helium Temperatures,” Sov. Phys. JETP 20, 44–49 (1965).
  21. N. Mott, H. Jones, The Theory of the Properties of Metals and Alloys (Dover, New York, 1958, p. 124.
  22. J. Petrakian et al., “Optical Properties of Liquid Tin Between 0.62 and 3.7 eV,” Phys. Rev. B 21, 3043–3046 (1980).
    [CrossRef]
  23. R. MacRae, E. Arakawa, M. Williams, “Optical Properties of Vacuum-Evaporated White Tin,” Phys. Rev. 162, 615–620 (1967).
    [CrossRef]
  24. J. Miller, “Optical Properties of Liquid Metals at High Temperatures,” Philos. Mag. 20, 1115–1132 (1969).
    [CrossRef]
  25. M. Otter, “Temperature Dependance of the Optical Constants of Heavy Metals,” Z. Phys. 161, 539–549 (1961).
    [CrossRef]
  26. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Sec. 13.4.1.
  27. Effectively there are two independent electron gas calculations, one on each side of the melting point.
  28. P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Artech House, Norwood, MA, 1987).

1980

J. Petrakian et al., “Optical Properties of Liquid Tin Between 0.62 and 3.7 eV,” Phys. Rev. B 21, 3043–3046 (1980).
[CrossRef]

1969

J. Miller, “Optical Properties of Liquid Metals at High Temperatures,” Philos. Mag. 20, 1115–1132 (1969).
[CrossRef]

1967

R. MacRae, E. Arakawa, M. Williams, “Optical Properties of Vacuum-Evaporated White Tin,” Phys. Rev. 162, 615–620 (1967).
[CrossRef]

1965

A. Golovashkin, P. Motulevich, “Optical Properties of Tin at Helium Temperatures,” Sov. Phys. JETP 20, 44–49 (1965).

1961

M. Otter, “Temperature Dependance of the Optical Constants of Heavy Metals,” Z. Phys. 161, 539–549 (1961).
[CrossRef]

J. Hodgson, “The Optical Properties of Liquid Germanium, Tin and Lead,” Philos. Mag. 6, 509–515 (1961).
[CrossRef]

1958

W. Rodgers, R. Powell, Tables of Transport Integrals, Natl. Bur. Stand. U.S. Circ.595 (1958).

1928

F. Bloch, Z. Phys. 52, 555 (1928).

E. Gruneisen, “Title,” Handb. Phys 13, 28–00 (1928).

1919

C. Kent, “The Optical Constants of Liquid Alloys,” Phys. Rev. 14, 459–489 (1919).
[CrossRef]

1890

P. Drude, Ann. Phys. 39, 504 (1890).

Arakawa, E.

R. MacRae, E. Arakawa, M. Williams, “Optical Properties of Vacuum-Evaporated White Tin,” Phys. Rev. 162, 615–620 (1967).
[CrossRef]

Beckman, P.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Artech House, Norwood, MA, 1987).

Bloch, F.

F. Bloch, Z. Phys. 52, 555 (1928).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Sec. 13.4.1.

Drude, P.

P. Drude, Ann. Phys. 39, 504 (1890).

Golovashkin, A.

A. Golovashkin, P. Motulevich, “Optical Properties of Tin at Helium Temperatures,” Sov. Phys. JETP 20, 44–49 (1965).

Gruneisen, E.

E. Gruneisen, “Title,” Handb. Phys 13, 28–00 (1928).

Hodgson, J.

J. Hodgson, “The Optical Properties of Liquid Germanium, Tin and Lead,” Philos. Mag. 6, 509–515 (1961).
[CrossRef]

Jones, H.

N. Mott, H. Jones, The Theory of the Properties of Metals and Alloys (Dover, New York, 1958, p. 124.

Kaye, G.

G. Kaye, T. Laby, Table of Physical and Chemical Constants (Longmans Green, London, 1966).

Kent, C.

C. Kent, “The Optical Constants of Liquid Alloys,” Phys. Rev. 14, 459–489 (1919).
[CrossRef]

Klein Wassink, R.

R. Klein Wassink, Soldering in Electronics (Electrochemical Publications, London, 1984), p. 105.

Laby, T.

G. Kaye, T. Laby, Table of Physical and Chemical Constants (Longmans Green, London, 1966).

Lish, E.

E. Lish, Lasers Tackle Tough Soldering Problems (Electronic Packaging & Production, June1984), p. 154.

MacRae, R.

R. MacRae, E. Arakawa, M. Williams, “Optical Properties of Vacuum-Evaporated White Tin,” Phys. Rev. 162, 615–620 (1967).
[CrossRef]

Miller, J.

J. Miller, “Optical Properties of Liquid Metals at High Temperatures,” Philos. Mag. 20, 1115–1132 (1969).
[CrossRef]

Mott, N.

N. Mott, H. Jones, The Theory of the Properties of Metals and Alloys (Dover, New York, 1958, p. 124.

Motulevich, P.

A. Golovashkin, P. Motulevich, “Optical Properties of Tin at Helium Temperatures,” Sov. Phys. JETP 20, 44–49 (1965).

Otter, M.

M. Otter, “Temperature Dependance of the Optical Constants of Heavy Metals,” Z. Phys. 161, 539–549 (1961).
[CrossRef]

Petrakian, J.

J. Petrakian et al., “Optical Properties of Liquid Tin Between 0.62 and 3.7 eV,” Phys. Rev. B 21, 3043–3046 (1980).
[CrossRef]

Powell, R.

W. Rodgers, R. Powell, Tables of Transport Integrals, Natl. Bur. Stand. U.S. Circ.595 (1958).

Rodgers, W.

W. Rodgers, R. Powell, Tables of Transport Integrals, Natl. Bur. Stand. U.S. Circ.595 (1958).

Spizzichino, A.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Artech House, Norwood, MA, 1987).

Williams, M.

R. MacRae, E. Arakawa, M. Williams, “Optical Properties of Vacuum-Evaporated White Tin,” Phys. Rev. 162, 615–620 (1967).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Sec. 13.4.1.

Ziman, J.

ℱ5(x)=∫0x[(z5ez)/(ez−1)2]dz, J. Ziman, Electrons and Phonons (Oxford U.P., London, 1979), p. 54.

Ann. Phys.

P. Drude, Ann. Phys. 39, 504 (1890).

Handb. Phys

E. Gruneisen, “Title,” Handb. Phys 13, 28–00 (1928).

Philos. Mag.

J. Miller, “Optical Properties of Liquid Metals at High Temperatures,” Philos. Mag. 20, 1115–1132 (1969).
[CrossRef]

Philos. Mag. 6

J. Hodgson, “The Optical Properties of Liquid Germanium, Tin and Lead,” Philos. Mag. 6, 509–515 (1961).
[CrossRef]

Phys. Rev.

C. Kent, “The Optical Constants of Liquid Alloys,” Phys. Rev. 14, 459–489 (1919).
[CrossRef]

R. MacRae, E. Arakawa, M. Williams, “Optical Properties of Vacuum-Evaporated White Tin,” Phys. Rev. 162, 615–620 (1967).
[CrossRef]

Phys. Rev. B

J. Petrakian et al., “Optical Properties of Liquid Tin Between 0.62 and 3.7 eV,” Phys. Rev. B 21, 3043–3046 (1980).
[CrossRef]

Sov. Phys. JETP

A. Golovashkin, P. Motulevich, “Optical Properties of Tin at Helium Temperatures,” Sov. Phys. JETP 20, 44–49 (1965).

Tables of Transport Integrals

W. Rodgers, R. Powell, Tables of Transport Integrals, Natl. Bur. Stand. U.S. Circ.595 (1958).

Z. Phys.

F. Bloch, Z. Phys. 52, 555 (1928).

M. Otter, “Temperature Dependance of the Optical Constants of Heavy Metals,” Z. Phys. 161, 539–549 (1961).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Sec. 13.4.1.

Effectively there are two independent electron gas calculations, one on each side of the melting point.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves From Rough Surfaces (Artech House, Norwood, MA, 1987).

N. Mott, H. Jones, The Theory of the Properties of Metals and Alloys (Dover, New York, 1958, p. 124.

ℱ5(x)=∫0x[(z5ez)/(ez−1)2]dz, J. Ziman, Electrons and Phonons (Oxford U.P., London, 1979), p. 54.

The Debye temperatures for Sn and Au are both ∼170 K, so that above room temperature T ≥ ϴD and ℱ5(x) converges to ℱ5 = ¼[(ϴD)/T]4.

R. Klein Wassink, Soldering in Electronics (Electrochemical Publications, London, 1984), p. 105.

G. Kaye, T. Laby, Table of Physical and Chemical Constants (Longmans Green, London, 1966).

Although the SnPb system as an alloy is not accurately described by the Bloch formula, the approximation of linear temperature dependence is used here for simplicity.

The integrating sphere accessory is the DRTA-9A made by Lapshere, Inc. as an accessory for the Perkin-Elmer Lambda-9 UV-VIS-NIR spectrometer. The actual reflectivity measurements were made at Labsphere. This schematic is a simplified version of a drawing from a Labsphere, Inc. product brochure.

The x-ray analyzer was calibrated by analyzing an NBS Standard Reference Material 1131, which is a 40:60 Sn:Pb standard. The analyzer gave a 38:62 composition and is thus regarded as accurate to ∼2%.

The soldering bath was purchased from Technic, Inc. This is a fluoborate sulfonic acid type system with ∼0.02% occluded carbon deposits.

E. Lish, Lasers Tackle Tough Soldering Problems (Electronic Packaging & Production, June1984), p. 154.

The solder paste is manufactured by Kester Solder, part R-229D, vacuum dried at 80°C for 30 min.

Kapton is a trademark of the Dupont Company. The measurement of the total reflectivity does not give information about the transmission properties of the film. It is assumed in table IV that the polyimide will be backed up with an opaque material so that the effective absorption may be obtained from the reflectivity by assuming that the sum of the absorption and reflectivity is unity.

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

The undesirable effects of splattering may be reduced by spatially scanning the laser during the heating period.

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Figures (14)

Fig. 1
Fig. 1

Schematic drawing of the integrating sphere optics that permit measurement of the total reflectivity of rough surfaces.

Fig. 2
Fig. 2

Total reflectivity for Sn in the wavelength range of 0.25–2.5 μm, as measured with an integrating sphere. The circles mark the values at 0.532 and 1.06 μm for both the bright and matte surfaces. The reduced reflectivity for the matte surface below ∼1.8 μm is due primarily to the surface roughness.

Fig. 3
Fig. 3

Total reflectivity for Au in the wavelength range of 0.25–2.5 μm. The circles mark the values at 0.532 and 1.06 μm for both the bright and matte surfaces. The reduced reflectivity for the matte surface below ∼1.8 μm is due primarily to the surface roughness.

Fig. 4
Fig. 4

Total reflectivity for matte Cu in the wavelength range of 0.25–2.5 μm. The circles mark the values at 0.532 and 1.06 μm.

Fig. 5
Fig. 5

Total reflectivity for SnPb in the wavelength range of 0.25–2.5 μm. The circles mark the values at 0.532 and 1.06 μm. The Sn:Pb composition was measured by an x-ray analyzer: (a) reflowed (51:43 with 6% Cu) by hot air leveling; (b) electroplated (47:53) at 80 ASF; (c) electroplated (47:53) at 100 ASF, (d) vacuum-dried paste (63:37).

Fig. 6
Fig. 6

Total reflectivity for FR-4 in the wavelength range of 0.25–2.5 μm. The circles mark the values at 0.532 and 1.06 μm.

Fig. 7
Fig. 7

Total reflectivity for polyimide in the wavelength range of 0.25–2.5 μm. The circles mark the values at 0.532 and 1.06 μm. The polyimide sample was a 50 μm thick sample of Kapton.

Fig. 8
Fig. 8

Electrical resistivity for SnPb, Sn, and Au in the temperature range from 0 to 1400 K. The open circles are data from the literature, and the solid line is the linear approximation. The SnPb composition is 60:40. A sharp increase in the resistivity is observed at the melting point of each metal.

Fig. 9
Fig. 9

Optical absorption, calculated as 1 − R of Sn as a function of temperature for a wavelength of 1.06 μm. The solid line is the electron gas calculation, and the points are data from the literature.

Fig. 10
Fig. 10

Optical absorption, calculated as 1 − R of Sn as a function of temperature for a wavelength of 0.532 μm. The solid line is the electron gas calculation, and the points are data from the literature.

Fig. 11
Fig. 11

Optical absorption, calculated as 1 − R of Au as a function of temperature for a wavelength of 0.532 μm. The solid line is the electron gas calculation, and the points are data from the literature.

Fig. 12
Fig. 12

Optical absorption, calculated as 1 − R of SnPb as a function of temperature for a wavelength of 0.532 μm. The solid line is the electron gas calculation, and the data point at 300 K is from Table III. The data point at 673 K is from the literature.

Fig. 13
Fig. 13

Optical absorption calculated from Eq. (17) of Sn as a function of temperature for a wavelength of 1.06 μm. The data point at 300 K is from Table II, and the specular data are used above the melting point.

Fig. 14
Fig. 14

Optical absorption calculated from Eq. (17) of Au as a function of temperature for a wavelength of 0.532 μm and several values of the parameter Ad. The data point at 300 K is from Table 1, and the specular data is used above the melting point.

Tables (4)

Tables Icon

Table I Metal Absorption at 0.532 μm (%)

Tables Icon

Table II Metal Absorption at 1.06 μm (%)

Tables Icon

Table III Solder Absorption (%)

Tables Icon

Table IV Polymer Absorption (%)

Equations (17)

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m + m β = e E
σ = N e 2 m ( β i ω ) .
σ = N e 2 m β ,
β = N e 2 m σ = N e 2 m ρ ,
ρ = 4 ρ 0 ( T ϴ D ) 5 5 ( ϴ D T ) ,
ρ = ρ 0 T ϴ D ,
R ( θ = 0 ) = ( n 1 ) 2 + k 2 ( n + 1 ) 2 + k 2 ,
̂ = ( n + i k ) 2 = 1 + 4 π i σ ω .
Re ( ̂ ) = n 2 k 2 = 1 = 1 ω p 2 ω 2 + β 2 ,
Im ( ̂ ) = 2 n k = 2 = ( β ω ) ω p 2 ω 2 + β 2 ,
ω p 2 = 4 π N e 2 m .
ρ opt = N e 2 m β ,
n = { ½ [ ( 1 2 + 2 2 ) 1 / 2 + 1 ] } 1 / 2 ,
k = { ½ [ ( 1 2 + 2 2 ) 1 / 2 1 ] } 1 / 2 .
A t = 1 R s ,
A d = Σ ( area of blacks holes ) total area ,
A t = 1 R s ( 1 A d ) ,

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