- Email: [email protected]
Modified O'Bryan ellipsometer (MOE) for film-substrate systems
Volume 27, number 1
OPTICS COMMUNICATIONS
October 1978
MODIFIED O'BRYAN ELLIPSOMETER (MOE) FOR FILM-SUBSTRATE SYSTEMS A.-R.M. ZAGHLOUL Electrical Engineering Department, Faculty of Engineering, Cairo University, Cairo, Egypt Received 31 May 1978
We present a modification of O'Bryan's return-path ellipsometer (J. Opt. Soc. Am. 26 (1936) 122) that extends its applicability to arbitrary surface retardations (not to be restricted to -+90° ) at angles of incidence other than the principal angles. This modified version uses a phase-retarding corner-reflector to return the light beam for a second reflection at the sample surface, with a single optical component acting as both polarizer and analyzer. The operation of the ellipsometer is visualized using the complex-plane representation of polarized light.
1. Introduction In 1936, O'Bryan introduced a simple ellipsometer to measure the optical properties of metals by detecting the principal angle of incidence ~ at which the ellipsometric angle A = -+7r/2 [1]. Recently, this ellipsometer has been used for film-substrate systems [2]. The main advantage of O'Bryan ellipsometer is that it employs one optical element, and that it is capable of fully characterizing the film-substrate system. In ref. [3], modifications that add more optical SIS
<~BS
components to the ellipsometer and fixes the angle of incidence are reported. These modifications still restrict the usefulness of the ellipsometer to the determination of two sample parameters only. In this communication, we present a different modification to the O'Bryan ellipsometer that allows the operation of the system at other than the principal angle of incidence (operation at different values of the eUipsometric angle A other than -+n/2). This modified version can be used to characterize fiknsubstrate systems as well as bare substrates.
2. The technique
M
Fig. 1. O'Bryan elfipsometer; L: light source, BS: beam splitter, P: polarizer, SS: sample surface, M: perpendicular mirror, D: detector, and 4>: angle of incidence.
When light is obliquely reflected from an optically isotropic surface, its two components with their electric field vector vibrating parallel (p) and perpendicular (s) to the plane of incidence undergo different phase shifts 6p and 6s, respectively. The difference between these two phase shifts is A = ~p -- ~s" The two field components, p and s, also undergo different amplitude attenuations upon reflection from the surface. The relative amplitude attenuation between the component waves is denoted as tan 4- Therefore, the ratio of the two complex reflection coefficients is given by
Rp/R s = tan ~ exp(jA).
(I)
Volume 27, n u m b e r 1
OPTICS COMMUNICATIONS
Now, if we fold back the reflected beam using a phase-retarding corner-reflector :bl, as shown in fig. 2, we can extinguish the light beam, after it is reflected a second time from the surface, using the same polarizing element and without need for a beam splitter. This is correct only if the corner reflector compensates for the relative phase shift produced by the surface A and if the polarizer azimuth equals the ellipsometric angle of the surface ¢. The null is obtained by adjusting the polarizer azimuth together with the angle of incidence. The ellipsometric function O of the sample surface, O = tan ~0 exp(jA), is the ratio between the complex numbers that represent the states of polarization S of the reflected and incident beams. If the incident beam is linearly polarized at an azimuth 0 (polarizer/ azimuth) its state of polarization is S 1 = cos 0/sin 0 = cot 0,
(2)
and the state of polarization of the reflected beam S 2 is S 2 = cot 0 tan ~ exp(i/x) = tan × exp(jA),
(3)
where tan r/= cot 0 tan ~. Let the ellipsometric function of the corner reflector (CR) be ,1 The corner reflector can be either a total-internal-reflection prism or be c o m p o s e d o f two single-reflection film-substrate retarders [5] fixed together at 90 ° w i t h t h e angle of incidence equal to 45 ° .
October 1978
OCR = exp(j 2~ICR). Accordingly, the state of polarization of the light beam emerging from the CR is S 3 = tan r/exp(j(A + 2~CR)).
S4 = tan ff tan r~ expO2(A + z~CR)).
(6)
Now, if0 = if,and z5 = --AfR,we have tan~7 = 1, and S 4 = tan ~k.
(7)
Eq. (7) implies that the light beam is now linearly polarized at 90 ° from the incident beam (S1). And the light reaching the detector is nulled 4:2 From the above, we find that at null the polarizer azimuth 0 equals the eUipsometric angle ff and the corner reflector ellipsometric angle ACR equals that of the surface. In the following, we present a complex-plane , 2 Eq. (7) is also satisfied w h e n 0 = ~0 and A = -+~r - ACR. To distinguish between the two values of A experimentally (A = - A C R and A = ±~r - ,aCR), if needed, we detect t h e a z i m u t h o f polarization of the beam between t h e two sides o f the CR, by use o f a polarizer, say. It is either positive, +45 °, (2~ = - A C R ) or negative, - 4 5 °, (ix = ±rr - ~ ? R ) , refer to fig. 4 and note , a Im
SS
+j
z
B
-- -L'.-tQndc
-i
.
(5)
Upon the second reflection from the sample surface, SS, the fight beam experiences O a second time and its state of polarization becomes
l/////'A////:./1////'/'//5.
Fig. 2. Modified O'Bryan eUipsometer (MOE); L: light source, P: polarizer~ SS: sample surface, CR: corner reflector, D: detector, a n d ¢: angle ot~incidenee. S1, $2, $3 and $4 are t h e states o f polarization of the incident beam, reflected beams, emerging b e a m f r o m CR, a n d light b e a m after second reflection from the sample surface (for expressions, see text).
(4)
D
C
Fig. 3. The complex-plane representation o f the operation of modified O'Bryan ellipsometer (MOE) at off null, see text. It shows t h e states o f polarization of the different stages of the light b e a m at off null.
Volume 27, number 1
OPTICS COMMUNICATIONS
October 1978 Irn.
$$
-1
+!
~ Re. ,tJ" "D
Y
-i -2A Fig. 4. (Left) The states of polarization of the different stages of the light beam in the complex plane at null for MOE. (Right) Schematic showing the polarization states superimposed on the path of the light beam of MOE. representation of the operation of the modified O'Bryan ellipsometer (MOE). In fig. 3, the state of polarization o f the incident light is represented by point A (linearly polarized light) at off null. After the first reflection from the surface, point A moves to point B (elliptically polarized light). Then the state of polarization of the incident light on the CR moves from point B to point C upon reflection from it (eiliptically polarized). Finally, we have the state o f polarization of the light beam after the second reflection from the surface at point D (elliptically polarized). Fig. 4 (left) represents the states o f polarization o f the different stages of the light beam in the complex plane at null. Fig. 4 (right) is a schematic that shows the polarization states superimposed on the path of the light beam ,3 The previous analysis holds for the case of 0 = - ~ with corresponding minor modifications.
3. Experimental considerations The corner reflector may also be designed to be ,3 For the case of A -- -+~r- ACR, the state of polarization B moves to C through the point -1 on the real axis (instead of point +1 for the case of A = - A c R ). Then it moves to point D as before.
angle-of-incidence-tunable, i.e., the same CR yields different retardations at different angles of incidence [5]. In either case, tunable or not, the folded beam is always parallel to the incident beam. And the ellipsometric function p of the sample surface is not changed for both beams. The relative angle between the light beam and the CR should always be kept constant as the angle of incidence is changed to achieve null. This ellipsometer yields itself easily to automation. Simply by providing motor drives for the angle of incidence and polarizer goneometers the automation is achieved. The accuracy and ultimate speed of the automated version has the same limitations o f other null-type ellipsometers.
References [1] H.M. O'Bryan, J. Opt. Soc. Am. 26 (1936) 122. [2] M. Yamamoto, Optics Commun. 10 (1974) 200. [3] T. Yamaguchi and H. Takahashi, Appl. Optics 15 (1976) 677. [4] A.-R.M. Zaghloul, R.M.A. Azzam and N.M. Bashara, J. Opt. Soc. Am. 65 (1975) 1043. [5] A.-R.M. Zaghloul, R.M.A. Azzam and N.M. Bashara, Opitcs Commun. 14 (1975) 260.
OPTICS COMMUNICATIONS
October 1978
MODIFIED O'BRYAN ELLIPSOMETER (MOE) FOR FILM-SUBSTRATE SYSTEMS A.-R.M. ZAGHLOUL Electrical Engineering Department, Faculty of Engineering, Cairo University, Cairo, Egypt Received 31 May 1978
We present a modification of O'Bryan's return-path ellipsometer (J. Opt. Soc. Am. 26 (1936) 122) that extends its applicability to arbitrary surface retardations (not to be restricted to -+90° ) at angles of incidence other than the principal angles. This modified version uses a phase-retarding corner-reflector to return the light beam for a second reflection at the sample surface, with a single optical component acting as both polarizer and analyzer. The operation of the ellipsometer is visualized using the complex-plane representation of polarized light.
1. Introduction In 1936, O'Bryan introduced a simple ellipsometer to measure the optical properties of metals by detecting the principal angle of incidence ~ at which the ellipsometric angle A = -+7r/2 [1]. Recently, this ellipsometer has been used for film-substrate systems [2]. The main advantage of O'Bryan ellipsometer is that it employs one optical element, and that it is capable of fully characterizing the film-substrate system. In ref. [3], modifications that add more optical SIS
<~BS
components to the ellipsometer and fixes the angle of incidence are reported. These modifications still restrict the usefulness of the ellipsometer to the determination of two sample parameters only. In this communication, we present a different modification to the O'Bryan ellipsometer that allows the operation of the system at other than the principal angle of incidence (operation at different values of the eUipsometric angle A other than -+n/2). This modified version can be used to characterize fiknsubstrate systems as well as bare substrates.
2. The technique
M
Fig. 1. O'Bryan elfipsometer; L: light source, BS: beam splitter, P: polarizer, SS: sample surface, M: perpendicular mirror, D: detector, and 4>: angle of incidence.
When light is obliquely reflected from an optically isotropic surface, its two components with their electric field vector vibrating parallel (p) and perpendicular (s) to the plane of incidence undergo different phase shifts 6p and 6s, respectively. The difference between these two phase shifts is A = ~p -- ~s" The two field components, p and s, also undergo different amplitude attenuations upon reflection from the surface. The relative amplitude attenuation between the component waves is denoted as tan 4- Therefore, the ratio of the two complex reflection coefficients is given by
Rp/R s = tan ~ exp(jA).
(I)
Volume 27, n u m b e r 1
OPTICS COMMUNICATIONS
Now, if we fold back the reflected beam using a phase-retarding corner-reflector :bl, as shown in fig. 2, we can extinguish the light beam, after it is reflected a second time from the surface, using the same polarizing element and without need for a beam splitter. This is correct only if the corner reflector compensates for the relative phase shift produced by the surface A and if the polarizer azimuth equals the ellipsometric angle of the surface ¢. The null is obtained by adjusting the polarizer azimuth together with the angle of incidence. The ellipsometric function O of the sample surface, O = tan ~0 exp(jA), is the ratio between the complex numbers that represent the states of polarization S of the reflected and incident beams. If the incident beam is linearly polarized at an azimuth 0 (polarizer/ azimuth) its state of polarization is S 1 = cos 0/sin 0 = cot 0,
(2)
and the state of polarization of the reflected beam S 2 is S 2 = cot 0 tan ~ exp(i/x) = tan × exp(jA),
(3)
where tan r/= cot 0 tan ~. Let the ellipsometric function of the corner reflector (CR) be ,1 The corner reflector can be either a total-internal-reflection prism or be c o m p o s e d o f two single-reflection film-substrate retarders [5] fixed together at 90 ° w i t h t h e angle of incidence equal to 45 ° .
October 1978
OCR = exp(j 2~ICR). Accordingly, the state of polarization of the light beam emerging from the CR is S 3 = tan r/exp(j(A + 2~CR)).
S4 = tan ff tan r~ expO2(A + z~CR)).
(6)
Now, if0 = if,and z5 = --AfR,we have tan~7 = 1, and S 4 = tan ~k.
(7)
Eq. (7) implies that the light beam is now linearly polarized at 90 ° from the incident beam (S1). And the light reaching the detector is nulled 4:2 From the above, we find that at null the polarizer azimuth 0 equals the eUipsometric angle ff and the corner reflector ellipsometric angle ACR equals that of the surface. In the following, we present a complex-plane , 2 Eq. (7) is also satisfied w h e n 0 = ~0 and A = -+~r - ACR. To distinguish between the two values of A experimentally (A = - A C R and A = ±~r - ,aCR), if needed, we detect t h e a z i m u t h o f polarization of the beam between t h e two sides o f the CR, by use o f a polarizer, say. It is either positive, +45 °, (2~ = - A C R ) or negative, - 4 5 °, (ix = ±rr - ~ ? R ) , refer to fig. 4 and note , a Im
SS
+j
z
B
-- -L'.-tQndc
-i
.
(5)
Upon the second reflection from the sample surface, SS, the fight beam experiences O a second time and its state of polarization becomes
l/////'A////:./1////'/'//5.
Fig. 2. Modified O'Bryan eUipsometer (MOE); L: light source, P: polarizer~ SS: sample surface, CR: corner reflector, D: detector, a n d ¢: angle ot~incidenee. S1, $2, $3 and $4 are t h e states o f polarization of the incident beam, reflected beams, emerging b e a m f r o m CR, a n d light b e a m after second reflection from the sample surface (for expressions, see text).
(4)
D
C
Fig. 3. The complex-plane representation o f the operation of modified O'Bryan ellipsometer (MOE) at off null, see text. It shows t h e states o f polarization of the different stages of the light b e a m at off null.
Volume 27, number 1
OPTICS COMMUNICATIONS
October 1978 Irn.
$$
-1
+!
~ Re. ,tJ" "D
Y
-i -2A Fig. 4. (Left) The states of polarization of the different stages of the light beam in the complex plane at null for MOE. (Right) Schematic showing the polarization states superimposed on the path of the light beam of MOE. representation of the operation of the modified O'Bryan ellipsometer (MOE). In fig. 3, the state of polarization o f the incident light is represented by point A (linearly polarized light) at off null. After the first reflection from the surface, point A moves to point B (elliptically polarized light). Then the state of polarization of the incident light on the CR moves from point B to point C upon reflection from it (eiliptically polarized). Finally, we have the state o f polarization of the light beam after the second reflection from the surface at point D (elliptically polarized). Fig. 4 (left) represents the states o f polarization o f the different stages of the light beam in the complex plane at null. Fig. 4 (right) is a schematic that shows the polarization states superimposed on the path of the light beam ,3 The previous analysis holds for the case of 0 = - ~ with corresponding minor modifications.
3. Experimental considerations The corner reflector may also be designed to be ,3 For the case of A -- -+~r- ACR, the state of polarization B moves to C through the point -1 on the real axis (instead of point +1 for the case of A = - A c R ). Then it moves to point D as before.
angle-of-incidence-tunable, i.e., the same CR yields different retardations at different angles of incidence [5]. In either case, tunable or not, the folded beam is always parallel to the incident beam. And the ellipsometric function p of the sample surface is not changed for both beams. The relative angle between the light beam and the CR should always be kept constant as the angle of incidence is changed to achieve null. This ellipsometer yields itself easily to automation. Simply by providing motor drives for the angle of incidence and polarizer goneometers the automation is achieved. The accuracy and ultimate speed of the automated version has the same limitations o f other null-type ellipsometers.
References [1] H.M. O'Bryan, J. Opt. Soc. Am. 26 (1936) 122. [2] M. Yamamoto, Optics Commun. 10 (1974) 200. [3] T. Yamaguchi and H. Takahashi, Appl. Optics 15 (1976) 677. [4] A.-R.M. Zaghloul, R.M.A. Azzam and N.M. Bashara, J. Opt. Soc. Am. 65 (1975) 1043. [5] A.-R.M. Zaghloul, R.M.A. Azzam and N.M. Bashara, Opitcs Commun. 14 (1975) 260.