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Aider: Angle-of-incidence-derivative ellipsometry and reflectometry
Volume
16, number
OPTICS
1
January
COMMUNICATIONS
AIDER: ANGLE-OF-INCIDENCE-DERIVATIVE
ELLIPSOMETRY
1976
AND REFLECTOMETRY
R.M.A. AZZAM Division of Hematology, Department of Internal Medicine, College of Medicine, University of Nebraska Medical Center, Omaha, Nebraska 681 OS, USA and Electrical Materials Laboratory*, College of Engineering, University of Nebraska, Lincoln, Nebraska 68508, USA Received
11 August
1975
A technique is proposed for the direct measurement of the derivatives a$/ap, aA/Q and ir?? /aq (or 3 In x /Q) of the ellipsometric (rl,, A) and reflectance (%) parameters of an optically isotropic surface with respect to the angle of incidence (9). A sinusoidal rotational oscillation of small amplitude 29 is applied to the sample around an axis in its surface perpendicular to the plane of incidence and the resulting ac/dc photoelectric signal-ratio 7 is measured in an ellipsometer with stationary polarizing and analyzing optics. I:rom three such measureFen ~1, ~~q?_?t three diffcrent settings of the ellipsometer optics, the amplitudes of the sinusoidal perturbations*Fj+, sA and E’)2 /.R of th%ellipsoyctr!: and reflectance parameters, caused by the angle-of-incidence oscillation 6~, can be determined. If 6 $, s^a and 8% /‘W are divided by S$, we get the desired derivatives a$/alp, aA/Q and 3 In 32 /ap. This technique of Anglcof-Incidence-Derivative Ellipsometry and Reflectometry (given the acronym AIDER) promises to open up new possibilities in surface optics particularly for the measurement of the optical properties of film-substrate systems.
1. Introduction
Conventional optical measurements on isotropic surfaces involve the determination of their ellipsometric ($, A) and reflectance (32) parameters at oblique incidence [l-6] . In this paper we propose a technique for the direct measurement of the angleof-incidence derivatives of these parameters, i.e., a$/&p, anlap and a%?/+ (or a ln% lap), where cpis the angle of incidence. The technique, which is given the acronym AIDER for Angle-of-Incidence-Derivative Ellipsometry and Reflectometry, promises to open up new possibilities in surface optics, particularly for the determination of the optical properties (refractive indices and extinction coefficients) and film thickness of film-covered substrates.
2. The technique The principle of AIDER is explained with refer* Supported
by the National
Science
Foundation.
ence to fig. 1. Consider an ellipsometer whose light beam is polarized by suitable polarizing optics P before it is incident on the sample S at an angle of incidence 9. The reflected beam is analyzed by analyzing optics A, and the transmitted flux is measured by a detector D to give a signal gD. With the polarizing
Fig. 1. Schematic of instrument for Angle-of-lncidenceDerivative Ellipsometry and Reflectometry (AIDER). L is a light source that gives a beam of unpolarized or circularly polarized light. P represents suitable polarizing optics. S is the sample under measurement which is rotationally vibrated around an axis perpendicular? the plane of incidence with frequency w and amplitude &+(the mean angle of incidence is ip). A represents suitable analyzing optics, and D is a photodetector which records a signal gD with dc and ac components 5 D and 69 D, respectively.
153
Volume
16, number
1
OPTICS COMMUNICATIONS
January
1976
and analyzing optics (P and A) stationary, a sizusoidal (pendulum-like) rotation of small amplitude 6~ and frequency o is applied to the sample around an axis in its surface passing through the point of reflection perpendicular to the plane of incidence. Because of angle-of-incidence oscillation,
(k= 1,3;**) are sets of parameters that characterize the polarizing and analyzing sections of the ellipsometer, respectively (they include the azimuth angles and optical properties of the optical components in these two sections). By taking the logarithmic differential of eq. (4), WCget
cp= (p + S&psin wt,
6 9,,&,
(1)
the ellipsometric and reflectance parameters of the surface ($, A,%) are sinusoidally modulated around --their quiscent (static) values ($,A,%) and have the same frequency as and arc in-phase with the mechanical rotation. so that
= (S%?/%) + EG S$ + CYa6A,
(5)
where cY+and 6, are psi and delta sensitivity ,fiuzctiutzs that relate changes of $ and A to corresponding changes of the detected photometric signal 9,. They arc obtained from the function F of eq. (4) by
$ = 3 + SA$sin wt, A = z + &A sin cd,
(2)
92 = 92 + &2 sin ot. Both the ellipse of polarization and intensity of the reflected beam also become modulated and an alternating-current (ac) component appears in the detected signal 9,
= 4,
+ fZIl, sin wt.
(3)
It is now essential to relatz the amplitude of the detector modulation signal 6 9,) to the amp$tudzs of th%ellipsomctric and reflectance signals S$, 6A and 6%. Below we detcrminc the relationship between changes 6 $, 6A, 6% caused by al!,! perturbation applied to the surface and the resulting change of the detector signal 6 9,. Because we assume an ellipsomcter with arbitrary polarizing and analyzing optics. the present treatment is more general than those previously developed in connection with electro-modulated ellipsometry [7,8] and anodic-oxide film growth studies [9,1Oj . Irrespective of the nature of the polarizing and analyzing optical elements in the two arms of the ellipsometer (P and A in fig. l), the detected signal can always be written as 9,] = KW-($.
A: pi, a&
that correspond to three different settings of the polarizing and (or) analyzing optics of the cllipsometer, we obtain three equations of the form of cq. (5) that can be put in matrix notation as
(4)
where (1) K is a proportionality factor; (2) 72 may be chosen to represent any one of the three reflectances 9? p, 92 s or %Zu for p-polarized, s-polarized or unpolarized light, respectively; (3) F is a function whose form depends on the ellipsometer optics and on the choice of W ; and (4) pi (i = 1.)2, * - -) and ak 1.54
In AIDER 6 $, &A, 6 %? and C 9, result from an angle-of-incidence oscillation; they are all sinusoidal, of the same frequency, and are all in phase [eqs. (1 )(3)] Therefore, eq. (5) can be used to directly relate their amplitudes. From three measurements ql, Q, q3 of the ac/dc signal ratio (modulation depth)
Eqs. (9) show how the three perturbations S$, S”n and S%?/% can be determined from three measurements of the ac/dc signal ratio Q, , q2, q3 at three
Volume
16, number
1
January
OPTICS COMMUNICATIONS
different settings of the ellips~leter pxlarizing and analyzing optics*. From S?$, 6A and 632 /?2, produAed by an angle-of-incidence oscillation of amplitude 6~, the derivatives
1976
given by Z$(PCS,q
2[tan~(l+cos2A)+sin2Asin(2P+Zi)] = _~~_~~~~~ ~~~~ 1 - cos 214 cos 2A + sin 2T sin (2P + a) sin 2A
’
(13a)
(lOa)
(1%)
can be evaluted. In eqs. (10) approximately equal(=) czn be replaced by exactly equal (=) in the limit when &‘O. It is important to observe that the quiscent values 5,x are needed to evaluate L$, and Za [eqs. (6)] ) hence the derivatives a$/alp and an/&p [eqs. (9a? b) and (lOa, b)] ; whereas the quiscent value % is needed only to evaluate a72/+, but not a ln9? /aq, where
a in37/aq
= (1/7qa7z/a(p,
(11)
as can be seen from eqs. (SC) and (10~). The distinction between different ellipsometer arrangements lies only in the different sensitivity functions Zilii and ZA [eqs. (5) and (6)] that need to be used. For example, in a polarizer--surface-analyzer (PSA) ellipsometer arrangement+, with the polarizer positioned at an azimuth of 4.5” from the plane of incidence, the sensitivity functions LY$and G’* are given by EJi (PSA) =
?ia(PSA)
=
2[tan$(l+cos2A)+cosXsin2A]
1 ~cos2;Lcos2A
+ sin2FcosXsin2A
’
~ sin 2T sin Z sin 2A 1 ~ cos2Tcos2A
+ sin2Tcosxsin2A
’
(123)
(12b)
where A is the analyzer azimuth measured from the plane of incidence. A can be set at three values to provide the three measurements ql, q2, q3 needed in eqs. (9). On the other hand, for a polarizer-compensator-surface-analyzer (PCSA) ellipsometer arrangement, in which the compensator acts as a X/4 retarder and is set with its fast axis at 45” from the plane of incidence, the sensitivity functions (Y, and ?YAare
t Additional measurements, in excess of three, may be taken to overdetermine the modulation signals 6-G) 6% and a&/?? which can then be found with higher accuracy. $ Both the polarizer and the analyzer are assumed to be ideal and linear (not elliptical).
where P and A arc the polarizer and analyzer azimuths measured from the plane of incidence. Eqs. (12) and (13) can be derived by straightforward use of Jones calculus to obtain expressions for the detected signal in the form of eq. (4) with %Z =%! s (the reflectance for s-polarized light), after which eqs. (6) are used to determine the sensitivity functions Zti and (YA. A possible source of error in AlDER is any contribution to the detected ac signal from the angular motion of the reflected beam (at twice the rate of sample rotation). This is $nimized with small angleof-incidence excursions (6ip < 0.1”) (which also represent a necessary condition for accurate differentiation), and by use of detectors that have uniform sensitivity over their active area covered by the beam.
3. Automation Repeated measurements of the ac/dc signal ratio q can be automated by mechanically or electro-optically altering the polarizing and (or) the analyzing optics of the ellipsometer. Precise synchronous detection of the ac component of the signal can be carried out by a lock-in amplifier. The measured values of both the ac and dc components of the detector signal can be digitized and fed to an on-line mini-computer for all subsequent data processing. Automatic angle-of-incidence scan can be used to measure angle-of-incidence “spectra” of a+/ap, aA/ap and a ln%/aq.
4. Applications
of AlDER
An isotropic film-substrate system is characterized by five parameters: the refractive index nf and extinction coefficient k+-of the film, the refractive index n, and extinction coefficient k, of the substrate, and the film thickness d. A single ellipsometric measurement of $, A at one angle of incidence is adequate, in prin155
Volume
16. number
1
OPTICS COMMUNICATIONS
ciplc, to d&ermine two of these five parameters only, provided the other three are known. Several methods have been suggested [ 111 to increase the acquired optical data so that all of the five parameters of a film--substrate system can be determined. We propose that AIDER be used at a single angle of incidence to supplement the ellipsometric angles $, A by the derivatives a $/&,o, aA/ap and 3 ln% /dip. ii/, A, a$/+, an/&p, 3 ln37 /&p provide an adequate set to determine all five parameters n,, k,, nf, k,, d of a film-substrate system. Like multiple-angle-ofincidence ellipsometry (MAlE) [ 12--141 , AIDER has the major advantage of not perturbing the film-substrate system under measurement (this is in contrast with methods that require changes in the ambient, film or substrate). Because the derivatives FI$/&p, aA/aq and 3 ln9’2jap are sensitive to very thin films [ 1.51 and small amounts of substrate absorption, AIDER is potentially more precise and accurate in determining the propertics of the filmsubstrate system. The present method is more general than that proposed by Paik and Bockris [ 161 (in which an additional reflectance measurement is made) in that it allows the optical parameters of both the film and substrate, instead of those of the film only, to be measured. This also obviates the need for accurate measurements on a cleaned substrate. We expect AIDER to be also useful for in situ measurements on surfaces in controlled environment provided that the mechanical oscillation of the sample is easy to achieve and that it does not significantly alter the surface process being observed.
156
January
1976
References [l] O.S. Heavens, Optical Properties [2] 13) [4
]
[5]
[6]
171 [Sl
of Thin Solid I:ilms (Dover, New York, 1965). A. VaSiEek, Optics of Thin Films (North-Holland, Amsterdam, 1960). A.V. Sokolov, Optical Properties of Metals (American Elsevier, New York, 1967). I:. Abel&, in: Physics of Thin Films, Eds. G. Hass and R.E. Thun (Academic Press, New York, 1971). E. Passaglia, R. Stromberg and J. Kruger, Eds., Ellipsometry in the Mcasurcment of Surfaces and Thin Films, Natl. Bur. Std. (U.S.) Misc. Pub. 1, No. 256 (U.S. Governmcnt Printing Office, Washington D.C., 1964). N.M. Bashara, A.B. Buckman and A.C. Hall, Eds., Proc. Symp. on Recent Developments in Ellipsometry (NorthHolland, Amsterdam, 1968). A.B. Buckman and N.M. Bashara, Phys. Rev. 174 (1968) 719. A.B. Buckman, Surface Sci. 16 (1969) 193; also in ref.
[61. I91 B.D. Cahan, J. Horkans and I:. Yeaser, Surface Sci. 37 (1973) 559. [lo1 J. Horkans. B.D. Cahan and E. Yeagcr, Surface Sci. 46 (1974) 1. 1111 I:.L. McCrackin and J.P. Colson, in ref. 151, pp. 61 t‘f. 1121 J.A. Johnson and N.M. Bashara, J. Opt. Sot. Am. 61 (1971) 457. [131 M.hl. Ibrahim and N.M. Bashara, J. Opt. Sot. Am. 61 (1971) 1622. I141 J. Shewchun and E.C. Rowe, J. Appl. Phys. 41 (1971) 4128. 1151 J.R. Zeidlcr, R.B. Kohles and N.M. Bashara, Appl. Opt. 13 (1974) 1591. 1161 W.K. Paik and J.O’M. Bockris, Surface Sci. 28 (1971) 61.
16, number
OPTICS
1
January
COMMUNICATIONS
AIDER: ANGLE-OF-INCIDENCE-DERIVATIVE
ELLIPSOMETRY
1976
AND REFLECTOMETRY
R.M.A. AZZAM Division of Hematology, Department of Internal Medicine, College of Medicine, University of Nebraska Medical Center, Omaha, Nebraska 681 OS, USA and Electrical Materials Laboratory*, College of Engineering, University of Nebraska, Lincoln, Nebraska 68508, USA Received
11 August
1975
A technique is proposed for the direct measurement of the derivatives a$/ap, aA/Q and ir?? /aq (or 3 In x /Q) of the ellipsometric (rl,, A) and reflectance (%) parameters of an optically isotropic surface with respect to the angle of incidence (9). A sinusoidal rotational oscillation of small amplitude 29 is applied to the sample around an axis in its surface perpendicular to the plane of incidence and the resulting ac/dc photoelectric signal-ratio 7 is measured in an ellipsometer with stationary polarizing and analyzing optics. I:rom three such measureFen ~1, ~~q?_?t three diffcrent settings of the ellipsometer optics, the amplitudes of the sinusoidal perturbations*Fj+, sA and E’)2 /.R of th%ellipsoyctr!: and reflectance parameters, caused by the angle-of-incidence oscillation 6~, can be determined. If 6 $, s^a and 8% /‘W are divided by S$, we get the desired derivatives a$/alp, aA/Q and 3 In 32 /ap. This technique of Anglcof-Incidence-Derivative Ellipsometry and Reflectometry (given the acronym AIDER) promises to open up new possibilities in surface optics particularly for the measurement of the optical properties of film-substrate systems.
1. Introduction
Conventional optical measurements on isotropic surfaces involve the determination of their ellipsometric ($, A) and reflectance (32) parameters at oblique incidence [l-6] . In this paper we propose a technique for the direct measurement of the angleof-incidence derivatives of these parameters, i.e., a$/&p, anlap and a%?/+ (or a ln% lap), where cpis the angle of incidence. The technique, which is given the acronym AIDER for Angle-of-Incidence-Derivative Ellipsometry and Reflectometry, promises to open up new possibilities in surface optics, particularly for the determination of the optical properties (refractive indices and extinction coefficients) and film thickness of film-covered substrates.
2. The technique The principle of AIDER is explained with refer* Supported
by the National
Science
Foundation.
ence to fig. 1. Consider an ellipsometer whose light beam is polarized by suitable polarizing optics P before it is incident on the sample S at an angle of incidence 9. The reflected beam is analyzed by analyzing optics A, and the transmitted flux is measured by a detector D to give a signal gD. With the polarizing
Fig. 1. Schematic of instrument for Angle-of-lncidenceDerivative Ellipsometry and Reflectometry (AIDER). L is a light source that gives a beam of unpolarized or circularly polarized light. P represents suitable polarizing optics. S is the sample under measurement which is rotationally vibrated around an axis perpendicular? the plane of incidence with frequency w and amplitude &+(the mean angle of incidence is ip). A represents suitable analyzing optics, and D is a photodetector which records a signal gD with dc and ac components 5 D and 69 D, respectively.
153
Volume
16, number
1
OPTICS COMMUNICATIONS
January
1976
and analyzing optics (P and A) stationary, a sizusoidal (pendulum-like) rotation of small amplitude 6~ and frequency o is applied to the sample around an axis in its surface passing through the point of reflection perpendicular to the plane of incidence. Because of angle-of-incidence oscillation,
(k= 1,3;**) are sets of parameters that characterize the polarizing and analyzing sections of the ellipsometer, respectively (they include the azimuth angles and optical properties of the optical components in these two sections). By taking the logarithmic differential of eq. (4), WCget
cp= (p + S&psin wt,
6 9,,&,
(1)
the ellipsometric and reflectance parameters of the surface ($, A,%) are sinusoidally modulated around --their quiscent (static) values ($,A,%) and have the same frequency as and arc in-phase with the mechanical rotation. so that
= (S%?/%) + EG S$ + CYa6A,
(5)
where cY+and 6, are psi and delta sensitivity ,fiuzctiutzs that relate changes of $ and A to corresponding changes of the detected photometric signal 9,. They arc obtained from the function F of eq. (4) by
$ = 3 + SA$sin wt, A = z + &A sin cd,
(2)
92 = 92 + &2 sin ot. Both the ellipse of polarization and intensity of the reflected beam also become modulated and an alternating-current (ac) component appears in the detected signal 9,
= 4,
+ fZIl, sin wt.
(3)
It is now essential to relatz the amplitude of the detector modulation signal 6 9,) to the amp$tudzs of th%ellipsomctric and reflectance signals S$, 6A and 6%. Below we detcrminc the relationship between changes 6 $, 6A, 6% caused by al!,! perturbation applied to the surface and the resulting change of the detector signal 6 9,. Because we assume an ellipsomcter with arbitrary polarizing and analyzing optics. the present treatment is more general than those previously developed in connection with electro-modulated ellipsometry [7,8] and anodic-oxide film growth studies [9,1Oj . Irrespective of the nature of the polarizing and analyzing optical elements in the two arms of the ellipsometer (P and A in fig. l), the detected signal can always be written as 9,] = KW-($.
A: pi, a&
that correspond to three different settings of the polarizing and (or) analyzing optics of the cllipsometer, we obtain three equations of the form of cq. (5) that can be put in matrix notation as
(4)
where (1) K is a proportionality factor; (2) 72 may be chosen to represent any one of the three reflectances 9? p, 92 s or %Zu for p-polarized, s-polarized or unpolarized light, respectively; (3) F is a function whose form depends on the ellipsometer optics and on the choice of W ; and (4) pi (i = 1.)2, * - -) and ak 1.54
In AIDER 6 $, &A, 6 %? and C 9, result from an angle-of-incidence oscillation; they are all sinusoidal, of the same frequency, and are all in phase [eqs. (1 )(3)] Therefore, eq. (5) can be used to directly relate their amplitudes. From three measurements ql, Q, q3 of the ac/dc signal ratio (modulation depth)
Eqs. (9) show how the three perturbations S$, S”n and S%?/% can be determined from three measurements of the ac/dc signal ratio Q, , q2, q3 at three
Volume
16, number
1
January
OPTICS COMMUNICATIONS
different settings of the ellips~leter pxlarizing and analyzing optics*. From S?$, 6A and 632 /?2, produAed by an angle-of-incidence oscillation of amplitude 6~, the derivatives
1976
given by Z$(PCS,q
2[tan~(l+cos2A)+sin2Asin(2P+Zi)] = _~~_~~~~~ ~~~~ 1 - cos 214 cos 2A + sin 2T sin (2P + a) sin 2A
’
(13a)
(lOa)
(1%)
can be evaluted. In eqs. (10) approximately equal(=) czn be replaced by exactly equal (=) in the limit when &‘O. It is important to observe that the quiscent values 5,x are needed to evaluate L$, and Za [eqs. (6)] ) hence the derivatives a$/alp and an/&p [eqs. (9a? b) and (lOa, b)] ; whereas the quiscent value % is needed only to evaluate a72/+, but not a ln9? /aq, where
a in37/aq
= (1/7qa7z/a(p,
(11)
as can be seen from eqs. (SC) and (10~). The distinction between different ellipsometer arrangements lies only in the different sensitivity functions Zilii and ZA [eqs. (5) and (6)] that need to be used. For example, in a polarizer--surface-analyzer (PSA) ellipsometer arrangement+, with the polarizer positioned at an azimuth of 4.5” from the plane of incidence, the sensitivity functions LY$and G’* are given by EJi (PSA) =
?ia(PSA)
=
2[tan$(l+cos2A)+cosXsin2A]
1 ~cos2;Lcos2A
+ sin2FcosXsin2A
’
~ sin 2T sin Z sin 2A 1 ~ cos2Tcos2A
+ sin2Tcosxsin2A
’
(123)
(12b)
where A is the analyzer azimuth measured from the plane of incidence. A can be set at three values to provide the three measurements ql, q2, q3 needed in eqs. (9). On the other hand, for a polarizer-compensator-surface-analyzer (PCSA) ellipsometer arrangement, in which the compensator acts as a X/4 retarder and is set with its fast axis at 45” from the plane of incidence, the sensitivity functions (Y, and ?YAare
t Additional measurements, in excess of three, may be taken to overdetermine the modulation signals 6-G) 6% and a&/?? which can then be found with higher accuracy. $ Both the polarizer and the analyzer are assumed to be ideal and linear (not elliptical).
where P and A arc the polarizer and analyzer azimuths measured from the plane of incidence. Eqs. (12) and (13) can be derived by straightforward use of Jones calculus to obtain expressions for the detected signal in the form of eq. (4) with %Z =%! s (the reflectance for s-polarized light), after which eqs. (6) are used to determine the sensitivity functions Zti and (YA. A possible source of error in AlDER is any contribution to the detected ac signal from the angular motion of the reflected beam (at twice the rate of sample rotation). This is $nimized with small angleof-incidence excursions (6ip < 0.1”) (which also represent a necessary condition for accurate differentiation), and by use of detectors that have uniform sensitivity over their active area covered by the beam.
3. Automation Repeated measurements of the ac/dc signal ratio q can be automated by mechanically or electro-optically altering the polarizing and (or) the analyzing optics of the ellipsometer. Precise synchronous detection of the ac component of the signal can be carried out by a lock-in amplifier. The measured values of both the ac and dc components of the detector signal can be digitized and fed to an on-line mini-computer for all subsequent data processing. Automatic angle-of-incidence scan can be used to measure angle-of-incidence “spectra” of a+/ap, aA/ap and a ln%/aq.
4. Applications
of AlDER
An isotropic film-substrate system is characterized by five parameters: the refractive index nf and extinction coefficient k+-of the film, the refractive index n, and extinction coefficient k, of the substrate, and the film thickness d. A single ellipsometric measurement of $, A at one angle of incidence is adequate, in prin155
Volume
16. number
1
OPTICS COMMUNICATIONS
ciplc, to d&ermine two of these five parameters only, provided the other three are known. Several methods have been suggested [ 111 to increase the acquired optical data so that all of the five parameters of a film--substrate system can be determined. We propose that AIDER be used at a single angle of incidence to supplement the ellipsometric angles $, A by the derivatives a $/&,o, aA/ap and 3 ln% /dip. ii/, A, a$/+, an/&p, 3 ln37 /&p provide an adequate set to determine all five parameters n,, k,, nf, k,, d of a film-substrate system. Like multiple-angle-ofincidence ellipsometry (MAlE) [ 12--141 , AIDER has the major advantage of not perturbing the film-substrate system under measurement (this is in contrast with methods that require changes in the ambient, film or substrate). Because the derivatives FI$/&p, aA/aq and 3 ln9’2jap are sensitive to very thin films [ 1.51 and small amounts of substrate absorption, AIDER is potentially more precise and accurate in determining the propertics of the filmsubstrate system. The present method is more general than that proposed by Paik and Bockris [ 161 (in which an additional reflectance measurement is made) in that it allows the optical parameters of both the film and substrate, instead of those of the film only, to be measured. This also obviates the need for accurate measurements on a cleaned substrate. We expect AIDER to be also useful for in situ measurements on surfaces in controlled environment provided that the mechanical oscillation of the sample is easy to achieve and that it does not significantly alter the surface process being observed.
156
January
1976
References [l] O.S. Heavens, Optical Properties [2] 13) [4
]
[5]
[6]
171 [Sl
of Thin Solid I:ilms (Dover, New York, 1965). A. VaSiEek, Optics of Thin Films (North-Holland, Amsterdam, 1960). A.V. Sokolov, Optical Properties of Metals (American Elsevier, New York, 1967). I:. Abel&, in: Physics of Thin Films, Eds. G. Hass and R.E. Thun (Academic Press, New York, 1971). E. Passaglia, R. Stromberg and J. Kruger, Eds., Ellipsometry in the Mcasurcment of Surfaces and Thin Films, Natl. Bur. Std. (U.S.) Misc. Pub. 1, No. 256 (U.S. Governmcnt Printing Office, Washington D.C., 1964). N.M. Bashara, A.B. Buckman and A.C. Hall, Eds., Proc. Symp. on Recent Developments in Ellipsometry (NorthHolland, Amsterdam, 1968). A.B. Buckman and N.M. Bashara, Phys. Rev. 174 (1968) 719. A.B. Buckman, Surface Sci. 16 (1969) 193; also in ref.
[61. I91 B.D. Cahan, J. Horkans and I:. Yeaser, Surface Sci. 37 (1973) 559. [lo1 J. Horkans. B.D. Cahan and E. Yeagcr, Surface Sci. 46 (1974) 1. 1111 I:.L. McCrackin and J.P. Colson, in ref. 151, pp. 61 t‘f. 1121 J.A. Johnson and N.M. Bashara, J. Opt. Sot. Am. 61 (1971) 457. [131 M.hl. Ibrahim and N.M. Bashara, J. Opt. Sot. Am. 61 (1971) 1622. I141 J. Shewchun and E.C. Rowe, J. Appl. Phys. 41 (1971) 4128. 1151 J.R. Zeidlcr, R.B. Kohles and N.M. Bashara, Appl. Opt. 13 (1974) 1591. 1161 W.K. Paik and J.O’M. Bockris, Surface Sci. 28 (1971) 61.