Pt, Ag, Ti, and W in the infrared and far infrared - MURI …muri.lci.kent.edu/.../NIM_Papers/Permittivity/1983_Ordal_optical.pdf105 14 r-In 10' SILVER x x 100 o 0 11 5 10 10I 102
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd,Pt, Ag, Ti, and W in the infrared and far infrared
M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward
Infrared optical constants collected from the literature are tabulated. The data for the noble metals andAl, Pb, and W can be reasonably fit using the Drude model. It is shown that -El(W) = E2(W) 2/(2w') at
the damping frequency c = c,. Also -El(w T) _ - (1/2) el(0), where the plasma frequency is op.
1. Introduction
Many measurements of the optical constants ofmetals have been made, primarily at near IR, visible,and UV wavelengths. Brandli and Sievers' havemeasured Au and Pb in the far IR. For the near and farIR we have compiled these data and have tabulated thereal and imaginary parts of the dielectric function, Eland e2, respectively, the index of refraction n and theextinction index k for each metal. Drude model2 pa-rameters giving a reasonable fit to the data are given forAu, Ag, Cu, Al, Pb, and W. In general, the Drude modelis not expected to be appropriate for transition metalsin the near and middle IR, but a good fit can be obtainedfor W with a Drude model dielectric function.
Weaver et al. 3 have compiled extensive tables oroptical properties of metals which have been recentlypublished. Most of their tables do not extend beyond12-yum wavelength, while our compilation extends to thelongest wavelength for which data are available. An-other standard compilation is that of Haas and Hadleyin the AMERICAN INSTITUTE OF PHYSICSHANDBOOK. 4 However, this includes data only upto 1967. Except for a few cases, the data presented hereare more recent.
Bennett and Bennett5 have shown that the Drudemodel fits the measured reflectance of gold, silver, andaluminum in the 3-30-/Im wavelength range with one
adjustable parameter; i.e., the Drude model parameterswere obtained from the dc resistivity and fitted with onefree electron per atom for gold and silver and 2.6 freeelectrons per atom for aluminum. Brandli and Sievershave shown that the Drude model is an excellent fit totheir far IR measurements on lead and provides a goodfit for gold with no adjustable parameters.
11. Definitions and Equations
In keeping with IR spectroscopic notation, allfrequencies will be expressed in cm-1 . The complexdielectric function es and the complex index of refrac-tion n, are defined as
(1)EC -el + ie2 n (n + ik)2 .
The Drude model dielectric function is2
C = E- - 2 . I
(1 + I co w T
where c, cop, and '-v, have units of cm-'. Separating thereal and imaginary parts yields
(3)
(4)
W2
el = E-co 2
2= ++ U2
In these equations, the plasma frequency6 is1 47rNe 2
1/2
,(cm-l) = _2rc me (5)
(2)
When this work was done all authors were with University of Mis-souri-Rolla, 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; S.E. Bell and R. R. Bell are now at Route 4, Box 124, Rolla, Missouri65401.
Fig. 1. Aluminum: -el(w) and 2(M) vs frequency. The solid lineis the Drude model. The data from Ref. 7 are: Shiles et al., o forboth -el and 2; Bennett and Bennett * for -El and 2; Schulz, 0 for
-el and 2-
10100 l2 103
FREQUENCY, W (CM')
00 102 103
FREQUENCY, W (CM'l
Fig. 3. Gold: -e,(w) and e2(W) vs frequency. The solid line is theDrude model. The data from Ref. 9 are: Bennett and Bennett, *for both -el and e2; Schulz, 0 for both; Motulevich and Shubin, forboth; Padalka and Shklyarevskii, 0 for both; Bolotin et al., x for both;
Brandli and Sievers, + for both; Weaver et al., A for both.
104
I nL
Z 3a: 10tv
10'
104 105
Fig. 2. Copper: -el(W) and 2(O) vs frequency. The solid line isthe Drude model. The data from Ref. 8 are: Schulz, 0 for both -eland 2; Lenham and Treherne, * for -el and 2; Robusto andBraunstein, o3 for both; Hageman et al., X for both; and Dold and
Mecke, A for both.
10a102 103
FREQUENCY, W (CM1)
Fig. 4. Lead: -e l(w) and e2(u) vs frequency. The solid line rep-resents the Drude model. The data from Ref. 10 are: Brandli andSievers, x for -el and + for 2; and Golovashkin and Motulevich, A
Fig. 5. Silver: -l(co) and E2(0) vs frequency. The solid line is theDrude model. The data from Ref. 11 are: Bennett and Bennett, *for both -el and e2; Schulz, 0 for both; and Hagemann et al., X for
both.
10L1
1 03
14)1
MM 2a: 10
101
1001o'
I I I I I
+ -E
+x
2 ExIn,
A +
A+
XMEn
xooA A.W0A
,< 4, , I A
0 D
X 40
COBRLT 0101
4,
1 1 1 I I I~~~~~~~~~~~~~4
103 104
FREQUENCT, W (CM')
104
14)
InZ 2
a: 10
14)
10I
100t02
3 103 104
FREQUENCT,W (CMI)
105
Fig. 7. Iron: -el(w) and f2() vs frequency. The data from Ref.13 are: Weaver et al., X for -El and A for E2; Bolotin et al., 0 for-El
and 0 for f2-
103
14)
In
za: 102
10'
100105
Fig. 6. Colbalt: -el(c) and 2(M) vs frequency. The data from Ref.12 are: Kirillova and Charikov, + for -el and 0 for e2; Johnson andChristy, 0 for -el and 0 for 42; and Weaver et al, x for -el and A for
e2.
105103 104
FREQUENCY. W (CM')
Fig. 8. Nickel: -el(co) and 42(W) vs frequency. The data from Ref.14 are: Lynch et al., X for-c and A for E2; Johnson and Christy, 0
Fig. 9. Palladium: -(W) and 42(C) vs frequency. The data fromRef. 15 are: Weaver and Benbow, 0 for -el and 0 for 2; Bolotin etal., + for -el and for 2; Johnson and Christy, X for -el and A for
42.
14)
10'
10 0 3
103 104
FREQUENCT, W (CM )
Fig. 11. Titanium: -el(w) and 42(W) vs frequency. The data fromRef. 17 are: Kirillova and Charikov, for both -el and 2; Lynch etal., A for both; Johnson and Christy, 0 for both; Kirillova and
Charikov, + for both; Bolotin et al., X for both.
106
105
104
14
In
102
100
10010O
Fig. 10. Platinum: -(co) and 42(W) vs frequency. The data fromRef. 16 are Weaver et al., A for -el and 03 for 42.
lOu 102 103
FREQUENCY, W (CMI)
Fig. 12. Tungsten: -l(w) and 42(W) vs frequency. The solid lineis the Drude model. The data from Ref. 18 are: Nomerovannaya et
al., 03 for both -el and 42; Weaver et al., A for both.
TABLE 1. Al, ALUMINUM (Continued)H. E. Bennett and J. M. Bennett, Optical Properties and ElectronicsStructure of Metals and Alloys, ed. F. Abeles (North-Holland, 1966),p. 175.
TABLE 3. Au, GOLDH. E. Bennett and J. M. Bennett, Optical Properties and ElectronicStructure of Metals and Alloys edited by F. Abeles (North-Holland,Amsterdam, 1966), p. 175.
TABLE 3. Au, Gold (Continued)J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch (with C. G. Olson),Physics Data, Optical Properties of Metals, (Fach-Information Zentrum,Kalsrube, FOR, 1981).
TABLE 5. Ag, SILVERH. E. Bennett and J. MI. Bennett in Optical Properties and ElectronicStructure o Metals and Alloys, edited by F. Abeles (North-Holland,Amsterdam, 1966), p. 175.
0,O 00 O 0 ,0N - N'tO't $d) M M-' ¢0N N X , Mo N M1 0 4 - C o 0 o0 0 U) 0 0 0 0 0X 0 0 0¢ t9 0 0 0 0 0 0 0 00X N - O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0, 0 0, ao N N ' 4
04 4 444z 44444 1Il 44 4 + 4 4 c4 4 44~ 4 4 44444 4 4 444 44 1 1V OaJ rN V M' 0 O 0 t N N N e4 N, Vsss Ne N M 0 -4 -- -' - - -O
oNvN-0'N
M co . m o eJ in It CO 0D h 0 1 1 0 *I t 0 M e N N N w es - - - o0 o: h v N- h. . . . * . * . . . * . . . * . . . . . . . . . * . . . . . ... . . . . . . . . . .
- In -r - - N - - - - - - - -oooooooooooooooooooooooooooo
d-N -If) -0 h Nd M t- h-s 0 M- m ew o 'O v m N- N go 'O M o 4D N -' t N o~ 0 h0 . .9 . . . * . . . . . . . . . . . . . . .00000000000000000000000000000000000000000000+ + + + I I 4 4 4 + + 4 4 4 4 + + 4 4 4 4 + 4 4 4 4 4 4LIILULULULAJLULII L U W W w l wII U l Uwl w w ww lU l Uwl L IwL IIL U LIIL I IlLIi wlU Lh ( h h m0 N 'O. 0U 4h-N- 0 , ' 0 D v o hd-o C'I So ' N 003.0 N h 'Io NM
co 0o m ODMN N N---o tD 1 In In In91 m m WV M M M M M M M MCv N N M N N i tNN NN0000000000000000000000000000000000000000000044444444444444444444444444444444444444444444
N N NM.N N N N NN N N NN N NNNNNN.3 4 - (~ 4 'O 0 'NNNNNNNNN'-0.00 ---------- h h- N N'N0NNNNMMM-MMMMMMMVVOID -'o0 3N N'0U V m )O'i- 4 4 4 - - - - h I I In In I I I I I I I I I I I I I I I I I I I I I I I I I I I I
LUULLLUU LUULLI LU LULU LUUUUU LILLUU LUL LrULt UL UL U r LUL UL U L t UL UL UL I
.oo o o o o o o o o oo o o o o o o o o o0 3 N N'lhJ0 ' 0 4 . 4l. .^ S ~l1.1t^1tJ . 4S t. . 4 u . C l^ 1. N^ ^l (S10li j <^]S S
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00e t 0 0 0 0 0 t t t t 6 N es N e t4 4 s 4 N ts N-NNoeotwcooeXl>rco0Nbno~-~tsc
L U L L LI L L L L U U U I L U U U U U L L L L L IL L L L L cLo- - - - - -U L U L NU L II e i t iII L t M M MUtLstJ L U
--- - - -00000000000000000000
444444444+44444
NN- n mW MMV10V0, NW(' 0'4 W VI) ) 0 4 . .0 0' (' 0 3 4.N(')-40ocbON-In 4.4.4.(1) C 1) CN - - -0 .CO 'o v )4
000000000000000000000000000000
00000000000000 0...............
N4.C)C'7'NW n ONto
VM.MMMMMVVMMNN-
NNNNNNNNN-----00000000000 000
04ON h In -'n 1)- N4
. ... . .... ..... .
N I0 0 0 0 0 0 0 00C 0 - e-N ' 1
VMMNNN---O¢N-
MMMMMMNNNNN-g--00000000000000.. . ...... ..
N-N-N-N--WVWN0-
N N N - 0 1)-- 4-0C0N
-o0000000000--000'000000 4o0oooo0
............... '-I -v ->) v 1 N 0 M N - -a N 0
N N~ N~ cn cX cX M! M MM
O , CD W, O - N 4 N WO
...............0 0 --- bl t) wtr 9C:-
0z
C
@
'V
IV
o
N
.
to
-jco
I 44a. > 'c 4'
a: o-40r4
0.,^LI.
m N
I-tD L
x
C
rX'a
EU
-00 ------ O0000000000000
44+4444444+44LUL USULULSULiU LU W0N0000con0nnoN 31 M N - 1 PI OD 1 0
TABLE 11. Ti, TITANIUM (Continued)G. A. Bolotin, A. N. Voloshinskii, M. M. Neskov, A. V. Sokolov, andB. A. Charikov, Phys. Met. and Met. 13, 823 (1962).
Table 13. Optical Parameters Found using a Drude Model Fit of the Experimental Dielectric Functions for Six Metals for which the Dielectric Functionscould be Fit; here w, Is the Frequency at which the Fit is Forced, and -e1(0) is -el (w) at dc; the Crossover Frequency Applies to -el e2
2f (cm1)for fit ofdata in IR
WT (cm- )IR fit
(cm1)IR fit
-Sl (O)p elT0
WT (cm )from dc
resistivitiesand p
W, (cm- )crossover on
el 2 lot
Noble Metals andAl and Pb
Al l.11x103 6.47xlO2 l.l9x1O 5 3.37xl04 6.45xlO2 7.00xlo2
Cu 2.O0x1O3 2.78xl02 6.38xl04 5.27xl04 1.15xl02 2.55xl02
Au 8.06xl0 2 2.16xlo2 7.25xl04 1.13xlO 5 1.93xlo2 2.16xlo2
Ag l.00x103 1.45xlo2 7.25xlO4 2.50xl05 1.41xlo2 1.52x102
Transition Metals
W 8.06xlO2 4.33xl02 4.84xl04 1.25xl04 2.16x102 4.30xl02
The one exception to this process was the measure-ments of Brandli and Sievers' for Au and Pb. Theyreported values of R(w)/Zo where Zo = (47r)/c. For thefar IR, Eq. (11) reduces to
Z &2) (14)
cw1 was obtained from this data using co, from the nearIR fit. This value of c, was used for gold and leadrather than the co obtained from the near IR fit.
We note from Eq. (12) the frequency for which -el(co)e2((.) is very nearly w = cT since -el >> 1. With w =
OT, both components (-El and 2) of the dielectricfunction are cw2/(2co 2). Thus the Drude parameters, co,and cop, can be determined at the crossover from co = c,and the value of the dielectric function. Note that-E 1(O) wco2/Cd2 ; so -/2el(0) - E(Cr)-
IV. Data
Figures 1-12 are plots of -EI(c) and e2(W) for thetwelve metals. The high frequency termination occurswhere the Drude model becomes invalid. The solidlines are calculated from the Drude model with theparameters listed in Table 13. Tables 1-12 present thecollected values of El, E2, n and k. Table 13 summarizesthe Drude model parameters from our fit (for Ag, Au,Cu, Al, Pb, and W) as well as co, calculated from cop andthe AIP Handbook 9 values of the dc resistivity. Di-electric functions for all metals considered in this articleexcept Pb have been tabulated by Weaver et al. for theUV, visible, and near IR.
Finally, we disclaim any physical signficance for theDrude model. The intent is only to parametrize theoptical constants for these metals even when there is
some question as to the physical meaning of the pa-rameters. The transition metals show interbandtransitions and cannot be fit with a Drude model in theIR (with the exception of W). Even the noble metalsin the IR can have small interband contributions to thedielectric constants.20
References1. G. Brandli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972).2. P. Drude, Theory of Optics (Longmans, Green, New York, 1922;
Dover, New York, 1968). A more modern reference is F. Wooten,Optical Properties of Solids (Academic, New York, 1972), p. 52.For the Drude model and surface impedance see B. Donovan,Elementary Theory of Metals (Pergamon, New York, 1967), p.220.
3. J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, "Part 1:The Transition Metals," "Part 2, Noble Metals, Aluminum,Scandium, Yttrium, the Lanthanides, and the Actinides," inPhysics Data, Optical Properties of Metals (Fachinformati-onszentrum 7514 Eggenstein-Leopoldshafen 2, Karlsruhe, Fed-eral Republic of Germany, 1981).
4. G. Haas and L. Hadley, in American Institute of PhysicsHandbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), p.6-118.
5. H. E. Bennett and J. M. Bennett, in Optical Properties andElectronic Structure of Metals and Alloys, F. Abeles, Ed.,(North-Holland, Amsterdam; Wiley, New York, 1966), Sec. 1.6,p. 175. For Ag, Au, and AL for co, they estimated 145, 216, and663 cm-', respectively.
6. For a single carrier type (electrons) the plasma frequency isas given in Eq. (5) where the dielectric constant is e- (the con-tribution from the core electrons at high frequencies). Often m*= m and c- = 1 are assumed. For discussion see H. Ehrenreichand M. H. Cohen, Phys. Rev. 1 5, 786 (1959); the last paragraphon p. 790 is most relevant.
7. Al: E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev.B 22, 1612 (1980); H. E. Bennett and J. M. Bennett, OpticalProperties and Electronic Structure of Metals and Alloys, F.Abeles, Ed. (North Holland, Amsterdam, 1966), p. 175; L. G.Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954).
8. Cu: L. G. Schulz, J. Opt. Soc. Am. 44, 357, 362 (1954); A. P.Lenham and D. M. Treherne, J. Opt. Soc. Am. 56,683 (1966); P.F. Robusto and R. Braunstein, Phys. Status Solidi B 107, 443(1981); H. J. Hageman, W. Gudat, and C. Kunz, J. Opt, Soc. Am.65, 742 (1975); B. Dold and R. Mecke, Optik 22, 435 (1965).
9. Au: H. E. Bennett and J. M. Bennett, Optical Properties andElectronic Structure of Metals and Alloys, F. Abeles, Ed.(North-Holland, Amsterdam, 1966), p. 75; L. G. Schulz, J. Opt.Soc. Am. 44, 357,362 (1954); G. P. Motulevich and A. A. Shubin,Sov. Phys. JETP 20, 560 (1965); V. G. Padalka and I. N. Shkly-arevskii, Opt. Spectrosc. 11, 285 (1961); G. A. Bolotin, A. N.Voloshinskii, M. M. Kirilbra, M. M. Neskov, A. V. Sokolov, andB. A. Charikov, Fiz. Met. Metalloved. 13, 823 (1962); G. Brandliand A. J. Sievers, Phys. Rev. B 5, 3550 (1972).
10. Pb: G. Brandli and A. J. Sievers, Phys. Rev. B 5, 3550 (1972); A.I. Golovashkin and G. P. Motulevich, Sov. Phys. JETP 26, 881(1968).
11. Ag: H. E. Bennett and J. M. Bennett, in Optical Properties andElectronic Structure of Metals and Alloys F. Abeles, Ed.(North-Holland, Amsterdam, 1966), p. 175; L. G. Schulz, J. Opt.Soc. Am. 44,357, and 362 (1954); H. J. Hagemann, W. Endat, andC. Kunz, J. Opt. Soc. Am. 65, 742 (1975).
12. Co: M. M. Kirillova and B. A. Charikov, Opt. Spectrosc. 17, 134(1964); P. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056(1974); J. H. Weaver, E. Colavita, D. W. Lynch, and R. Rosei,Phys. Rev. B 19, 3850 (1979).
13. Fe: J. H. Weaver, E. Colavita, D. W. Lynch, and R. Rosei, Phys.Rev. B 19, 3850 (1979); G. A. Bolotin, M. M. Krillova, and V. M.Mayevskiy, Phys. Met. Mettalogr. USSR 27, No. 2, 31 (1969).
14. Ni: D. W. Lynch, R. Rosei, and J. H. Weaver, Solid State Com-mun. 9,2195 (1973); P. B. Johnson and R. W. Christy, Phys. Rev.B 9, 5056 (1974).
15. Pd: J. H. Weaver and R. L. Benbow, Phys. Rev. B 12,3509 (1975);G. A. Bolotin, M. M. Kirillova, L. V. Nomerovannaya, and M. M.Noskov, Fiz. Met. Mettalloved. 23,463 (1967); P. B. Johnson andR. W. Christy, Phys. Rev. B 9, 5056 (1974).
16. Pt: J. H. Weaver, Phys. Rev. B 11, 1416 (1975); J. H. Weaver, C.G. Olson, and D. W. Lynch, Phys. Rev. B 10, 501 (1974).
17. Ti: M. M. Kirillova and B. A. Charikov, Opt. Spectrosc. 17, 134(1964); D. W. Lynch, C. G. Olson, and J. H. Weaver, Phys. Rev.B 11, 3617 (1975); P. B. Johnson and R. W. Christy, Phys. Rev.B 9, 5056 (1974); M. M. Kirillova and B. A. Charikov, Phys. Met.15, 138 (1963); G. A. Bolotin, A. N. Voloshinskii, M. M. Noskov,A. V. Sokolov, and B. A. Charikov, Phys. Met. Metallogr. USSR13, 823 (1962).
18. W: L. V. Nomerovannaya, M. M. Kirillova, and M. M. Noskov,Opt. Spectrosc. 17, 134 (1964); J. H. Weaver, D. W. Lynch, andC. G. Olson, Phys. Rev. B 12,1293 (1975).
19. J. Babiskin and J. R. Anderson, in American Institute of PhysicsHandbook, (McGraw-Hill, New York, 1972), p. 9-39.
20. G. R. Parkins, W. E. Lawrence, and R. W. Christy, Phys. Rev. B23, 6408 (1981).
This work was partially supported by the U.S. Army,DAAK-11-82-C-0052. We gratefully acknowledge thevaluable advice of Jean M. Bennett, David Begley,David Bryan, Kul Bhasin, and W. F. Parks.
7 Interferogram showing creditable accuracy of the concave 8 Grinding the cone using a flat diamond wheel and the correctsurface. tilt angle. The work rotates at 100 rpm, the diamond wheel at