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Refractive index of thin films of ZnSe in the IR
Thin Solid Filrns, 112(1984) L1 L4
L1
Letter Refractive index of thin films of ZnSe in the IR S. AHMED AND E. E. KHAWAJA* Pakistan Institute of Nuclear Science and Technology, P.O. Nilore, Islamabad (Pakistan) (Received August 31, 1983; accepted November 22, 1983)
The method devised by Khawaja t of determining the refractive indices of thin transparent films from measurements of the transmittance at normal incidence was applied to a study of evaporated layers of ZnSe. Previously Thutupalli and Tomlin 2 have determined the optical properties of thin films of ZnSe in the spectral range 0.5-2.5 lain. In the present work the measurements are extended further into the IR. The films are non-absorbing in the spectral region investigated; therefore we are concerned with the refractive index only. The refractive index nt of a transparent film of thickness dl on a transparent substrate of refractive index n2 can be determined from a single measurement of the transmission at normal incidence 1. For a wavelength 2, the transmittance Tf of the film into the s u b s t r a t e is given by H e a v e n s 3 as
Tf
n2 (1 +gl)2(1 q-g2) 2 n o 1 +g12g2 2 + 2 g i g 2 cos(2y 0
(1)
where /'/0 2 --y/12 gt = - (n o q- nl) 2 n12--n22 g2 = - (n 1 + n2) 2 71-
2rcnldl 2
a n d n o is the refractive index of air. If Tf, d: a n d n 2 are k n o w n , then in principle n 1 can be d e t e r m i n e d from the a b o v e relation. A n expression giving an explicit value of n 1 c a n n o t be obtained. H o w e v e r , the e q u a t i o n m a y be solved by a n u m e r i c a l m e t h o d as was discussed by K h a w a j a 1. F o l l o w i n g the p r o c e d u r e a d o p t e d by K h a w a j a , the refractive index of thin films of Z n S e was d e t e r m i n e d in the spectral range from 2.5 to 14.0 ~tm. The films of Z n S e of thickness 1.0-2.0 ~tm were p r e p a r e d on o p t i c a l l y p o l i s h e d s u b s t r a t e s in the form of wedges of angle 3 ° by e v a p o r a t i o n from a t a n t a l u m b o a t in a * Present address: Physics Department, University of Petroleum and Minerals, Dhahran, Saudi Arabia. 0040-6090/84/$3.00
© Elsevier Sequoia/Printed in The Netherlands
L2
I.ETTERS
vacuum of 10 -5 Torr. The rate of evaporation was about 0.08 p m m i n i. The substrates were cleaned ultrasonically in an acetone bath and then ion bombarded in a low pressure gas discharge, prior to the evaporation. During the deposition the substrates were rotated to improve the uniformity of the films. The normal incidence transmittance was measured in air using a Perkin-Elmer IR 850 spectrophotometer. The use of a wedge substrate ensured that reflections from the back of the substrate were deflected out of the optical path of the instrument so that multiple reflections in the substrate do not affect the measurements. However, the wedge angle was sufficiently small for the transmission across the back face to be given accurately enough by the transmittance formulae for normal incidence. Figure 1 is an example of the transmission curves for an uncoated KBr substrate and a ZnSe film on a KBr substrate. It should be noted that the transmittance Tf in eqn. (1) is the transmittance into the substrate. The measured transmittance Tin, f --- T f T s , where Ts is the transmittance across the back face of the substrate and is 4non2/(n o + n2) 2. 100
90
•~- 70 J b
60
50 l.O
145
)25
)0.5
85
65
1,5
25
Wavelength (l~m)
Fig. I. Measuredtransmissions Tin. s for an uncoated KBr substrate (curvea) and Tinsfor a ZnSefilmon a KBr substrate (curveb). The measured transmittance Tm,s of the uncoated substrate in terms of the refractive index of the substrate is given by Tm's = Ts2 =
non 2 2 (n O-k n2) 2
(2)
The refractive index n2 for various wavelengths was calculated from the measured transmittance using the above equation. The present results for KBr were found to be in agreement with the following dispersion formula given for KBr by Stephens et al. 4
0.007676 22
nz z = 2.361323--0.00031149722--5.8613 x 10 ~2'*q--
where 2 is in micrometres.
0.0156569 22 --0.0324
LETTERS
L3
F r o m the measured transmittance the dispersion curve shown in Fig. 2 was obtained for ZnSe films using eqn. (1), beginning with an approximate film thickness and then adjusting this value in an attempt to obtain a closed dispersion curve 1. The approximate thickness was obtained from the following relation dx =
1
2122
(3)
4nl 2 1 - 2 2
where 21 and 22 are the wavelengths corresponding to the consecutive minima and maxima of the transmittance curve• It may be mentioned that the value of n x used in eqn. (3) was estimated from the minima of the Tt curve (Tf,ml.lma) which are given by 4n12n2 Tf'minima -- (tll 2 "l'-/12) 2
(4)
(no = 1). The above relation is valid for n~ > n 2, which is true in the present case•
3.2 2.8 .~_ 2/,
. . . . . . . . .
~: 2.0
',,••
-°
•-
. ....
°•
16
• ••°°•,,.,, i
i
i
i
13
12
1)
10
i
,"
i
8
7
i
i
6
5
t,
i
i
3
2
Wavelength (prn)
Fig. 2. Dispersion curve showing multiple solutions and proper continuity, derived from the data of Fig. 1.
The dots in Fig. 2 represent the multiple solutions of the refractive indices for the corresponding wavelengths derived from the data of Fig. 1 for a ZnSe film of thickness 1.56 tam. Ten films of ZnSe which varied in thickness were studied in an attempt to displace spectrally the maximum of the transmittance curve which is the region of possible large errors in the calculated refractive index s. The average dispersion is shown in Fig. 2 by the continuous curve• Calculations show that the m a x i m u m errors in the refractive index, due to errors of 1~o in dl, +0.002 in T and +0.005 in n2, do not exceed 1~o. The refractive index is found to be 2.4 at 14 p.m and increases to 2.42 as the wavelength decreases to 2.5 p.m. Thutupalli and Tomlin 2 have measured the refractive indices of thin films of ZnSe in the spectral range from 0.5 to 2.5 p.m. They obtained a refractive index of about 2.42 at 2.5 p.m. However, Marple 6 measured a refractive index of 2.45 at 2.5 p.m for a sample in the form of a prism of pure crystalline ZnSe, using the s t a n d a r d spectroscopic methods• It is a c o m m o n observation that a material in the bulk form has a slightly higher refractive index than that for thin films of the same material• The method in which the film thickness is determined simultaneously with the refractive index from the measurement of transmittance at normal incidence has
L4
LETTERS
been a p p l i e d successfully to films of ZnSe. T h u s e x p e r i m e n t a l d a t a on the refractive index of Z n S e has been e x t e n d e d further into the IR. S.A. gratefully a c k n o w l e d g e s the a w a r d C o m m i s s i o n fellowship.
of a P a k i s t a n
A t o m i c Energy
1 E.E. Khawaja, J. Phys. D, 9 (1976) 1939. 2
G . K . M . ThutupalliandS. G. Tomlin, J. Phys. D, 9(1976) 1639.
3 O.S. Heavens, Optical Properties of Thin Solid Films, Butterworths, London, 1955. 4 R.E. Stephens, E. K. Phyler, W. S. Rodney and R. J. Spindler, J. Opt. Soc. Am., 43 (1953) 110. 5 6
E.E. KhawajaandS. G. Tomlin, J. Phys. D, 8(1975) 581. D . T . F . Marple, J. Appl. Phys.,35(1964) 539.
L1
Letter Refractive index of thin films of ZnSe in the IR S. AHMED AND E. E. KHAWAJA* Pakistan Institute of Nuclear Science and Technology, P.O. Nilore, Islamabad (Pakistan) (Received August 31, 1983; accepted November 22, 1983)
The method devised by Khawaja t of determining the refractive indices of thin transparent films from measurements of the transmittance at normal incidence was applied to a study of evaporated layers of ZnSe. Previously Thutupalli and Tomlin 2 have determined the optical properties of thin films of ZnSe in the spectral range 0.5-2.5 lain. In the present work the measurements are extended further into the IR. The films are non-absorbing in the spectral region investigated; therefore we are concerned with the refractive index only. The refractive index nt of a transparent film of thickness dl on a transparent substrate of refractive index n2 can be determined from a single measurement of the transmission at normal incidence 1. For a wavelength 2, the transmittance Tf of the film into the s u b s t r a t e is given by H e a v e n s 3 as
Tf
n2 (1 +gl)2(1 q-g2) 2 n o 1 +g12g2 2 + 2 g i g 2 cos(2y 0
(1)
where /'/0 2 --y/12 gt = - (n o q- nl) 2 n12--n22 g2 = - (n 1 + n2) 2 71-
2rcnldl 2
a n d n o is the refractive index of air. If Tf, d: a n d n 2 are k n o w n , then in principle n 1 can be d e t e r m i n e d from the a b o v e relation. A n expression giving an explicit value of n 1 c a n n o t be obtained. H o w e v e r , the e q u a t i o n m a y be solved by a n u m e r i c a l m e t h o d as was discussed by K h a w a j a 1. F o l l o w i n g the p r o c e d u r e a d o p t e d by K h a w a j a , the refractive index of thin films of Z n S e was d e t e r m i n e d in the spectral range from 2.5 to 14.0 ~tm. The films of Z n S e of thickness 1.0-2.0 ~tm were p r e p a r e d on o p t i c a l l y p o l i s h e d s u b s t r a t e s in the form of wedges of angle 3 ° by e v a p o r a t i o n from a t a n t a l u m b o a t in a * Present address: Physics Department, University of Petroleum and Minerals, Dhahran, Saudi Arabia. 0040-6090/84/$3.00
© Elsevier Sequoia/Printed in The Netherlands
L2
I.ETTERS
vacuum of 10 -5 Torr. The rate of evaporation was about 0.08 p m m i n i. The substrates were cleaned ultrasonically in an acetone bath and then ion bombarded in a low pressure gas discharge, prior to the evaporation. During the deposition the substrates were rotated to improve the uniformity of the films. The normal incidence transmittance was measured in air using a Perkin-Elmer IR 850 spectrophotometer. The use of a wedge substrate ensured that reflections from the back of the substrate were deflected out of the optical path of the instrument so that multiple reflections in the substrate do not affect the measurements. However, the wedge angle was sufficiently small for the transmission across the back face to be given accurately enough by the transmittance formulae for normal incidence. Figure 1 is an example of the transmission curves for an uncoated KBr substrate and a ZnSe film on a KBr substrate. It should be noted that the transmittance Tf in eqn. (1) is the transmittance into the substrate. The measured transmittance Tin, f --- T f T s , where Ts is the transmittance across the back face of the substrate and is 4non2/(n o + n2) 2. 100
90
•~- 70 J b
60
50 l.O
145
)25
)0.5
85
65
1,5
25
Wavelength (l~m)
Fig. I. Measuredtransmissions Tin. s for an uncoated KBr substrate (curvea) and Tinsfor a ZnSefilmon a KBr substrate (curveb). The measured transmittance Tm,s of the uncoated substrate in terms of the refractive index of the substrate is given by Tm's = Ts2 =
non 2 2 (n O-k n2) 2
(2)
The refractive index n2 for various wavelengths was calculated from the measured transmittance using the above equation. The present results for KBr were found to be in agreement with the following dispersion formula given for KBr by Stephens et al. 4
0.007676 22
nz z = 2.361323--0.00031149722--5.8613 x 10 ~2'*q--
where 2 is in micrometres.
0.0156569 22 --0.0324
LETTERS
L3
F r o m the measured transmittance the dispersion curve shown in Fig. 2 was obtained for ZnSe films using eqn. (1), beginning with an approximate film thickness and then adjusting this value in an attempt to obtain a closed dispersion curve 1. The approximate thickness was obtained from the following relation dx =
1
2122
(3)
4nl 2 1 - 2 2
where 21 and 22 are the wavelengths corresponding to the consecutive minima and maxima of the transmittance curve• It may be mentioned that the value of n x used in eqn. (3) was estimated from the minima of the Tt curve (Tf,ml.lma) which are given by 4n12n2 Tf'minima -- (tll 2 "l'-/12) 2
(4)
(no = 1). The above relation is valid for n~ > n 2, which is true in the present case•
3.2 2.8 .~_ 2/,
. . . . . . . . .
~: 2.0
',,••
-°
•-
. ....
°•
16
• ••°°•,,.,, i
i
i
i
13
12
1)
10
i
,"
i
8
7
i
i
6
5
t,
i
i
3
2
Wavelength (prn)
Fig. 2. Dispersion curve showing multiple solutions and proper continuity, derived from the data of Fig. 1.
The dots in Fig. 2 represent the multiple solutions of the refractive indices for the corresponding wavelengths derived from the data of Fig. 1 for a ZnSe film of thickness 1.56 tam. Ten films of ZnSe which varied in thickness were studied in an attempt to displace spectrally the maximum of the transmittance curve which is the region of possible large errors in the calculated refractive index s. The average dispersion is shown in Fig. 2 by the continuous curve• Calculations show that the m a x i m u m errors in the refractive index, due to errors of 1~o in dl, +0.002 in T and +0.005 in n2, do not exceed 1~o. The refractive index is found to be 2.4 at 14 p.m and increases to 2.42 as the wavelength decreases to 2.5 p.m. Thutupalli and Tomlin 2 have measured the refractive indices of thin films of ZnSe in the spectral range from 0.5 to 2.5 p.m. They obtained a refractive index of about 2.42 at 2.5 p.m. However, Marple 6 measured a refractive index of 2.45 at 2.5 p.m for a sample in the form of a prism of pure crystalline ZnSe, using the s t a n d a r d spectroscopic methods• It is a c o m m o n observation that a material in the bulk form has a slightly higher refractive index than that for thin films of the same material• The method in which the film thickness is determined simultaneously with the refractive index from the measurement of transmittance at normal incidence has
L4
LETTERS
been a p p l i e d successfully to films of ZnSe. T h u s e x p e r i m e n t a l d a t a on the refractive index of Z n S e has been e x t e n d e d further into the IR. S.A. gratefully a c k n o w l e d g e s the a w a r d C o m m i s s i o n fellowship.
of a P a k i s t a n
A t o m i c Energy
1 E.E. Khawaja, J. Phys. D, 9 (1976) 1939. 2
G . K . M . ThutupalliandS. G. Tomlin, J. Phys. D, 9(1976) 1639.
3 O.S. Heavens, Optical Properties of Thin Solid Films, Butterworths, London, 1955. 4 R.E. Stephens, E. K. Phyler, W. S. Rodney and R. J. Spindler, J. Opt. Soc. Am., 43 (1953) 110. 5 6
E.E. KhawajaandS. G. Tomlin, J. Phys. D, 8(1975) 581. D . T . F . Marple, J. Appl. Phys.,35(1964) 539.