金屬材料折射率

1、Optical properties of the metals Al, Co, Cu9 Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infraredM. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. WardInfrared optical constants collected from the literature are tabulated. The data for the

2、 noble metals and Al, Pb, and W can be reasonably fit using the Drude model. It is shown that 一“(3)« “(3)a o>p/(2w?) at the damping frequency o> = o>r. Also 一“(3 J e 一 (%) “(0), where the plasma frequency is 3pI. IntroductionMany measurements of the optical constants of metals have bee

3、n made, primarily at near IR, visible, and UV wavelengths. Brandli and Sievers1 have measured Au and Pb in the far IR For the near and far IR we have compiled these data and have tabulated the real and imaginary parts of the dielectric function, and(2> respectively, the index of refraction n and

4、the extinction index k for each metal. Drude model2 parameters giving a reasonable fit to the data are given for Au, Ag, Cu, Al, Pb, and W In general, the Drude model is not expected to be appropriate for transition metals in the near and middle IR, but a good fit can be obtained for W with a Drude

5、model dielectric functionWeaver et al.3 have compiled extensive tables or optical properties of metals which have been recently published. Most of their tables do not extend beyond 12-jum wavelength, while our compilation extends to the longest wavelength for which data are available Another standar

6、d compilation is that of Haas and Hadley in the AMERICAN INSTITUTE OF PHYSICS HANDBOOK, However, this includes data only up to 1967. Except for a few cases, the data presented here are more recentBennett and Bennett6 have shown that the Drude model fits the measured reflectance of gold, silver, and

7、aluminum in the 3-30-gm wavelength range with oneWhen this work was done all authors were with University of Mis souri-RolIa, Physics Department, Rolla, Missouri 65401; C. A. W Krebs is now with McDonnell Douglas Astronautics Company, Electrooptic Technology, P.O. Box 516, St. Louis Missouri 63166;

8、S. E. Bell and R. R. Bell are now at Route 4. Box 124, Rolla, Missouri 65401.Received 12 October 1982.0003-6935/83/071099-21S01.00/0.© 1983 Optical Society of Americaadjustable parameter; i.e., the Drude model parameters were obtained from the de resistivity and fitted with one free electron pe

9、r atom for gold and silver and 2.6 free electrons per atom for aluminum. Brandli and Sievers have shown that the Drude model is an excellent fit to their far IR measurements on lead and provides a good fit for gold with no adjustable parameters.II. Definitions and EquationsIn keeping with IR spectro

10、scopic notation, all frequencies will be expressed in cm"1. The complex dielectric function c and the complex index of refrac tion nc are defined ass 3 (n + ik)2.(1)The Drude model dielectric function isO>2 +where o>p, and have units of cm-1. Separating the real and imaginary parts yields

11、In these equations, the plasma frequency6 is圭隱匕where N is the free electron density, e is the electron charge, m* is the effective mass of the electrons, and is the high frequency dielectric constant. The damping frequency expressed in cm"1 isWrCcm"1) »(6)2rcrwhere r is the electron l

12、ifetime in seconds and c is the velocity of light. Note that for low frequenciesFREQUENCY. W （CM-1）Fig. 1. Aluminum: -q（o>） and “（3） vs frequency. The solid line is the Drude model The data from Ref. 7 are: Shiles et al., for both -1 and 切;Bennett and Bennett for 一“ and 切；Schulz, 0 for and切FREQUE

13、NCY, UJ （CK*1）Fig. 2. Copper: -“（3）and “（3）vs frequency The solid line is the Drude model. The data from Ref. 8 ore; Scliulz, Q for both and <2； Lenham and Treherne, * for and 切；Robusto and Braunstein, for both; Hageman et al.9 X for both; and Dold and Mecke, a for both.FREQUENCY. W （CN*lJFig. 3.

14、 Gold: “（3）and “（3）vs frequency The solid line is the Drude model. The data from Ref. 9 are: Bennett and Bennett* * for both -and 切；Schulz,。for both; Motulevich and Shubin, for both; Padalka and Shklyarevskii, O for both; Bolotin et al.9 X for both;Brandli and Sievers, + for both; Weaver et al.9 a f

15、or bothFREQUENCY,W （CM-1）Fig. 4. Lead: “（3）and “（3）vs frequency The solid line represents the Drude model The date from Ref. 10 are: Brandli and Sievers, X for and + for and Golovashkin and Motulevich, a for and for.1FREQUENCY.W （CM ）Fig. 5 Silver: -“（3）and “（3） vs frequency. The solid line is the D

16、rude model. The data from Ref. 11 are: Bennett and Bennett, * for both -and “； Schulz, Q for both; and Hagemann et al,9 X for both Fig. 7. Iron: c（3）and 切（3）vs frequency The data from Ref.13 are: Weaver et al., X for and A for “； Bolotin et al, for i and O for 切N' 1 11 1 '1°*x+D +O XAgX

17、%一XCOBALT®oe. 1 1 1.iiiio2io3ioMio5FReQUENCY.W （CM-1）Fig. 8. Nickel: 一“（3）and 切（3）vs frequency. The data from Ref.14 are: Lynch et al. t X for “ and A for 的;Johnson and Christy, 0 for -and O for 切FREQUENCY,UJ （CH*1）Fig. 6. Colbalt:-勺（3）and 切（3）vs frequency. The data from Ref.12 are: Kirillova a

18、nd Charikov, + for 一“ and for 切；Johnson andChristy, 0 for 一“ and O for q; and Weaver et al9 X for -and A for切io2io31OMio5FREQUENCY,UJ (CM*1)Fig. 9. Palladium: -j(w) and "(3) vs frequency. The data from Ref. 15 are: Weaver and Benbow, 0 for q and O for 2； Bolotin et al.9 + for and for 2； Johnson

19、 and Christy, X for 1 and A forFREQUENCY, W (CMH)Fig. 11. Titanium: r 1(3) and “(3) vs frequency. The data from Ref. 17 are: Kirillova and Charikov, for both 一“ and “； Lynch et al.9 for both; Johnson and Christy, O for both; Kirillova and Charikov, + for both; Bolotin et al. X for both.<M 屮o sIFR

20、EQUEHCYtUJ (CH*1)Fig. 12. Tungsten: -i(a>) and 切(3)vs frequency The solid line is the Drude model The data from Ref. 18 are: Nomerovannaya et al.9 for both and 切；Weaver et aL9 A for both.Fig 10. Platinum: 一1(3) and 2(0) vs frequency The data fromRef. 16 are Weaver et al.9 a for and for 切TABLE 1.

21、Al 9 ALUMINUME. Shi 1es9 T. Sasaki 9 M. Inokuti 9 and D. Y. Smith, Phys. R B 22, 1612 <1980>(cm-1)X<Pm)-C 1<2nK3.23E*02 3.3?E*02 3.71E*02 4.03E+02 4.36E*02 4.68E*02 5.00E*02 5.32E*02 5.81E*02 6.45E*02 7. 10E*02 7.74E*02 8.87E*02 1.05E*03 1.21E*03 1.37E*03 1.61E*03 2.02E*03 2.42E*03 2.82E

22、*03 3.23E*03 4.84E*03 6.45E*03 8.07E*03 1.21E>04 1.41E*043.10E*01 2.95E*01 2.70E*01 2.48E*01 2.30E>01 2.14E*01 2.00E*01 1.88E*01 1.72E*01 1.55E*01 1.41E*01 1.29£*01 1.13E*01 9.54E*00 8.27E*00 7.29E*00 6.20E*00 4.?6E*00 4.13E*00 3.54E*00 3.lOEOO 2.07E*00 1.55E400 1.24E*00 8.27E-01 6.20E-01

23、3.18E*04 3.01E*04 268E>04 2.43E*042. 14E*04 1.95E*04 1.80E*04 1.66E*04 1.50E*04 1.32E*04 1.18E*04 1.05E*04 8.77E*03 6.93E+03 5.58E*03 4.51E*03 3.39E*03 2.25E*03 1.63E*03 1.24E*03 ?.71E*02 4.53E*02 2.52E*02 1.54E*026. 15E*0i 5.42E>014.02E*04 3.62E*04 3.03E*04 2.59E*04 2.24E*04 2.01E*04 1.79E*04

24、 1.60E*04 1.38E*04 1.13E*04 ?.49E*03 7.87E*03 5.94E*03 4.07E*03 2.86E*03 2.0553 1.39E*03 8.28E>02 5.54E*02 3.87E*02 2.80E*02 ?.73E*01 4.61E*01 3.02E*01 4.56E>01 1.95E*019.86E401 9.22E401 8.26E401 7.50E401 6.93E401 6.52E401 6.07E401 5.67E401 5.20E401 4.58E401 4.09E401 3.62*01 3.02E401 2.35E401

25、1.86E401 1.49E401 1.17E401 8.59E*00 6.76E400 5.44E400 4.45E400 2.27E400 1.44E400 1.21E400 2.75E400 1.30E4002.04E4021. ?6E>02 1.83E>02 1.73E*02 1.62E*02 1.54E*02 1.47E*02 1.41E*02 1.33E402 1.24E*02 1.16E*02 1.0E*02 9.84E401 8.65E*0i 7.70E>01 6.88E*01 5.94E*01 4.82E*01 4. 10E*01 3.56E*01 3.15

26、E*012. 14E*01 i.60E*01 1.25E*01 8.31E*00 7.48E*00TABLE i. Al, ALUMINUM (Continued)H. E. Bennett and J. M. Bennett 9 Optical Properties and Eltronics Structure of Metals and Al 1oysf ed. F Abeles (North-Hol and9 1966> 9 p. 175.X<Pm>-< 1<2nk3.13E*023.20E*012.60E*045.56E*041.33E>022.0

27、9E*023.23E*023.10E*012.58E*045.31E*041.29E*022.06E*023.33E*023.00E*012.56E*045.08E*041.23E*022.03E*023.45E*022.90E*012.54E*044.84E241.21E*022.00E*02357E*022.80E*012.47E+044.5?E*041.17E*021.94E*023.70E*022.70E+012.45E*044.36E*041.13E>021.93E*023.85E*022.60E*012.38E*04412E*041.09E+021.8?E*02400E>

28、;022.50E*012.36E*043.91E>041.05E*021.84E*024.17E>022.40E*012.31E*043.64E*041.00E*021.82E*024.35E*022.30E*012.25E*043.42E*04?.60E*011.78E*024.55E*022.20E*012.l?E*043.18E*049.15E*011.74E*024.7Q022.10E*012. 10E*042.93E*048.68E*011.69E*025.00E*022.00E*012.05E*042.71E*048.21E*011.65E*025.26E*021.90

29、E*011.96E*042.47E*047.73E*011.60E*025.56E*021.80E*011.88E*042.24E*047.24E*011.55E*025.88E4021.70E*011.80E*042.02E>046.74E*011.30E*026.25E*02160E4011.69E*041.79E*046.23E*011.44E*026.47E021.50E*011.58E*041.58E*045.71E*011.38E*027.14E*021.40E*011.47E*041.37E*045.19E*011.32E*027.69E*021.30E*011.37E*0

30、41.18E*044.67E*011.26E*028.330021.20E*011.24E*04?.88E*034.1SE*O11.19E*02夕.0夕E*021.10E*011. 10E*040.060033.63E*0i1.11E*O21.00E*03l.OOEOl?.84E*036.49E*033.12E*011.04E*021. 11E*O39.00E*008.41E*035.02E*032.63E*019.54E*011.25E*038.00E*007.02E*033.72E*032.15E+0!8.65E*01TABLE 1. Al9 ALUMINUM (Continued)L.

31、G. Schulz9 J. Opt. Soc. Am. 44, 357 <1954) and 362 <1954).-< 1<2nk1.05E*049.50E-016.92E*012.98E*011.75E*00850E*001. 11E>O49.00E-015.54E*013.02E>011.96E*007.70E*001.18E*048.50E-014.48E*012.97E*012.08E*007.15E*001.25E*048.00E-014.57E*012.81E*011.9?E*007.05E*001.33E-047.50E-014.75E*01

32、2.56E*011.80E*007.12E*001.43E*047.00E-014.66E*012.17E*01l.SSEOO7.00E*001.54E*046.50E-014.20E*011.64E*011.24E*006.60E001.47E*046.00E-013.51E*011.16E>019.70E-016.00E*001.82E>045.50E-012.77E*018.09E*007.60E TH5.32E*002.00E>045.00E-012.27E*015.95E*006.20E-014.80E*002.22E044.50E-011.84E>014.2

33、3E*004.20E-014.32E*002.S0E*044.00E-011.32E*013.14E>004.00E-013.92E*00TABLE 2. Cu9 COPPERL. G. Schulz, J. Opt. an. 44f 357 and 362 (1954).XCPm)-< 1<2nk1.0SE>049.50E-013.87E*011.62E*001.30E-016.22E>001. 11E*O49.00E-013.43E*011.52E*001.30E-015.86E>001.18E*048.50E-012.99E*011.31E*001.2

34、0E5.47E*001.25E*048.00E-012.57E*011.22E*001.20E-015.07E*001.33E*047.50E-012.13E*011.11E4001.20E-014.62E*00i.43E>047.00E-011.74E*01l.OOEOO1.20E-014. 17E*001.54E*046.50E-011.33E*019.49E-011.30E-013.65E*001.67E*046.00E-01?.40E*001.04E*001.70E-013.07E*00l.82E>045.50E-015.34E*00348EfOO7.20E-012.42E

35、*002.00E*045.00E-01S.08E*004.26E*008.80E-012.42E*00222E>044.50E-014.08E*003.83E*008.70E-012.20E*00TABLE 2. Cut COPPER (Continued)A. P. Lenham and D. M. Treh«rn«9 J. Opt Soc Am. 56f 683 <1944>.X<Mm)5.00E*022.00E*011.33E*043.3<SE*021.80E*011.13£*046.29E*021.60E*019.00E*03

36、7. 14E*021.40E*016.80E*038.330021.20E4015.05E*031.00E03l.OOEOl3.S0E*03!.2SE*038.00E*002.20E*031.67E*036.00E>001.30E*032.00E*03S.OOEOO1.00E032.50E*034.00E*006.22027.6IE*033. 16E*011.20E*026.liE*032.76E4011. 1 t£>024.64E*032.37E*019.78E*013.36E*031.98E*01848E>012.2?E*031.57E*017.28E*0114

37、OEO31.16E*016.03£*017.28E*027“E004.75E*013.24E*024.46E*003.63E>011.40E*022.21E*003. 17E*01e.eoeoi1.76E*002.50E*01TABLE 2« Cu9 Copper (Continued)P. F. Robusto and Braunst»in9 Phys. Stat Sol <b> 107, 443 (1981)(D<cm- >)X(Rm)1.56E*046.40E-017.69E*001.67E*046.00E-015.98E*00

38、i.79E>045.60E-014.09E*001.92E*045.20E-013.71E*002.08E*044.80E-013.lOEOO2.27E*044.40E2.39E*002.50£*044.00E-011.81E*001.70E*003.04E2.79E*001.70E*003.44E-012.47E*002.20E*005.26E-012.09E*006.99E*001.45E002.41E*nn7.01E*001.51E*002.32£*006.79E*001.5SE*002.1?E*OO5.92E*001.48E>002.00E>00T

39、ABLE 2. Cut COPPER (Continued)H. J. Hagwmann 9 W. Gudat 9 and C. Kunz 9 J. Opt Soc. Am. 63, 742 <1975)G)< cm->>-< 1<2nk8.07E*021.24E>014.24E*034.25E*032.?7E*017.16E*014.03E>032.48E*003.06E*026.03E*011.71E*001.76E>018.07E*031.24E*007. I7E*O17.44E*004.40E-018.46E*001.21E*048

40、.27E-012.76E*012.74E*002.60E-015.26E*001.37E*047.29E-011.96E4011.95E*002.20E-014.43E*001.47.08E-01t.80E*011.79E*002. 10E-014.25E*00i.45E*046.89E-011.63E*0i1.70E*002. 10E-014.04E*00U49E*046.70E-011.48£*011.69E*002.20E-013.83E*001.53E*046.53E-011.34E*0l1.54E*002. 10E-013.67E*001.61E*044.20E-011.0

41、4E>011.75E*002.70E-013.24E*00TABLE 2. Cu9 COPPER (Continued)B. Dold and R. Meckef Optik 22, 435 <1965).X<Rm>-< 142nk1.00E*03l.OOEOl2.27E*031. 14E*031.16E*014.90E>011.11E*O39.00E*001.99E*039.05E*029.90E*004.57E*011.25E*038.00E*001.66E*036.72E*028. 10E*004.15E>011.43E*037.00E*001.

42、31E*034.71E*026.40E*003.68E011.67E*036.00E*009.99E*023.17E*024.95E*003.20E*012.00E*03S.OOEOO6.95E*021.92E*023.60E*002.66E012.50E*034.00E*004.56E*021.05E*022.45E*002. 15E*013.33E*033.00E*002.54E*024.80E*01150E*001.60E*015.00E*032.00E*001.12E*021.80E*018.50E-011.06E*016.67E*03l.SOEOO6.37E*01?.28E*005.

43、80E-018.00E*008.00E*031.25E*004.46£*016.57E*004.90E-016.70E*00TABLE 3. Au, GOLDH. E. Bennett and J. M. Bennett 9 Optical Properties and Electronic Structure of Metals and Al 1oys edi ted by F. Abeles (North-Hol 1 and, Amsterdmy 1966)9 p. 175.(a)(cm-i)X<J*m)1<2nk3. 13E*02 3.33E*02 3.57E*02

44、 3.85E*02 4.17E*02 4.55E>02 5.00E*02 5.56E*02 4.25E*027. 14E*02 8.33E*02 1.00E*03 1.25E*03 1.43E*03 1.47E*03 2.00E*03 2.50E*03 3.33E*033.20E*01 3.00E*01 2.80E*01 2.60E*01 2.40E*01 2.20E*01 2.00E*0i 1.80E*01 1.60E>01 1.40E*01 1.20E*01 l.OOEOl 8.00E*00 7.00E*00 4.00E*00 5.00E*00 4.00E*00 3.00E*0

45、03.6?E*04 3.37E*04 3.06E*04 2.73E*04 2.41E*04 2.08E*04 1.77E*04 1.48E*04 1.22E*04 沢51E*03 7. i4E*03 5.05E+03 3.29E*03 2.54E*03 1.88E4.03 1.31E*03 839E*02 4-75E*022.54E*04 2.17E*04 1.84E*04 1.53E*04 1.24E*04 ?.89E*03 7.67E*03 5.78E*03 419E03 2.86E*03 1.84E*03 1.0?E*03 5.48E*02 3.83E*02 2.42£*02

46、1.41E*02 7.25E*01 3.07E*016.28E*01 5.66E*01 5.05E*01 4.46E*01 3.89E*01 3.34E*01 2.82E*01 2.33E*01 1.87E*01 1.45E*01 1.08E*01 7.62E*00 4.93E*00 3.79E*00 279£00 1.95E*00 1.25E*00 7.04E-012.02E*02 1.92E*02 1.82E>02 1.71E*02 1.60E*02 1.48E*02 l«36E*02 1.24E*02 1.12E*02 9.86E*01 8.52E*01 7.1

47、5E*01 5.76E*01 5.05E*01 4.34E*01 3.62E*01 2.90E*012. 18E*01TABLE 3. Au 9 Gold (Continued)L. 6. Schulz 9 J Opt Soc. Am.357 and 362 < 1954) 0<cm->)X(Pm>1<2nk1.03E*049.50E-013.72E>012.32E*001.90E-016. 10E4001.11E*O49.00E-013.27E*012.06E*001.80E-015.72E*00125E*048.00E-012.34E*011.55E&g

48、t;001.60E-014.84E*001.43E>047.00E-011.57E*011.35E*001.70E-013.97E*001.67E*046.00E-018.77E*001.37E*002.30E-012.?7E*002.00E*045.00E-012.68E*003.09E*008.40E-011.84E*00222E*044.50E-011.57E*005.24E*001.40E4001.89E*00TABLE 3. Au, GOLD (Continued)G. P. Motulevieh and A. A. Shubin9 Soviet Phy. JETP 20, 5

49、40 <1945>.0<cm- >>X(Hm>8.33E402 1.00E*03 1.25E*03 1.67E*03 2.00E*03 2.50E*03 3.33E*03 4.00E*03 5.00E403 6.67E403 1.00E*041.20E401 l.OOEOi 8.00E00 6.00E00 5.00E*00 4.00E*00 3.00E*00 2.50E>00 2.00E>00 1.50E>00 1.000006.24E>03 4 420032. 2E*03 1.72E*03 1.23E*03 7.74E*02 4.4

50、0E*02 2.99E*02 1.93E*02 1.08E>02 4.50E*012.48E403 1.55E*03 8.54E*023. ?2E*02 2.30E*02 1.14E*024. ?1E*O1 2.84E>01 1.52E*01 7.43E*00 3.01E4001.54E>01 1.15E*01 7.82e00 4.70E*00 3.27E400 2.04E*00 1.17E*00 8.20E-01 5.46E-01 3.57E-01 2.24E-018.05E*01 6.75E*01 3.46e01 4.17E*01 3.52E*01 2.79E*012.

51、10E*01 1.73E*01 1.3?E*01 1.04E*01 6.71E*00TABLE 3. Au9 GOLD (Continued)V. G. Padalka and I N. Shklyarevski i 9 Opt Spectr. U.S.S.R. 11, 285 <19dl>w<cm *X<Hm>?.09E*02 1.00E*03 1.11EO3 1.25E*03 1.43E*03 1.67E*03 2.00E*03 2.50E*03 3.33E*03 5.00E*03 1.00E*041. 10E401 l.OOEOl ?.OOEfOO 8.00

52、E>00 7.00E*00 6.00E00 5.00E*00 4.00E00 3.00E400 2.00E*00 l.OOEOO3.31E*03 2.80E03 2.32E03 1.87E*03 1.45E*03 1.08E*03 7.62E*024. ?1E*O2 2.78E*02 1.25E*02 3.10E*011.01E037. F1E*O2 6.04E*02 4.39E*02 3.04E*02 1.99E*02 1.21E402 6.62E013. llEOl 1.21E*01 3.46E*008.71E*00 7.41E*00 6.21E*00 5.05E*003. ?7E*

53、003. D1E*OO 2.19E400 1.49E*00 9.30E-01 5.40E-01 3.10E013.82E*01 n34E(M 4.86E>01 4.35E*01 3.83E*01 3.30E*01 2.77E*01 2.22E>01 1.67E*01 1.12E*01 5.58E*00TABLE 3. Au, GOLD (Continued)6 A. Bolotini A. N. Voloshinski i 9 M. M. Neskov, A. V. Sokolov9 and B. A. Charikov, Phys. Met. andd 823 <1962>.(i)< cm-1)X(Rm)-< 1<2nk1.05E*03?.50E>002.44E>031.10E*031.09E>015.06E*011.110039.00E*002.1?E*O39.58E*02l.OOEOl4.7?E*011.18E*038.S0E*001.98E*038.86E>02?.72E>004.S6E011.25E*038.00E*001.87E*036.?5E*027.?0E*004.40E4011.430037.00E*001.51E*