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A simple immersion method to determine the refractive index of thin silica films
A SIMPLE I M M E R S I O N M E T H O D TO D E T E R M I N E THE
R E F R A C T I V E INDEX OF T H I N SILICA FILMS A. M. KAUFFMAN
Central Research Laboratory, Associated Electrical Industries Limited, Rugby, Warwickshire (Gt. Britain) (Received January 24, 1967; revised March 20, 1967)
SUMMARY
A simple and precise method is described for finding the refractive index of certain thin films using a novel immersion technique.
INTRODUCTION
When a transparent isotropic solid is immersed in a liquid, reflection and refraction at the surface of the solid in general lessen, and indeed cease completely in the special case when the refractive index of the liquid equals that of the solid. If the solid is a thin interference film, the intensity of the fringe pattern diminishes on immersion, vanishing entirely in the special case, since its formation depends on reflection at the solid-liquid boundary. This fringe disappearance phenomenon is exploited in the present method, which gives quite precise results using rudimentary apparatus. In outline the method is as follows. The film, deposited on a substrate, is immersed in a liquid medium and suitable fringes are observed in monochromatic light with the unaided eye. The refractive index of the medium is gradually altered h~ s i t u by mixing in drops of another liquid until the fringes, which have been progressively fading owing to reduced interfacial reflections, vanish altogether. At this point the refractive index of the medium ideally equals that of the film and can be measured easily, using an Abb6 refractometer or the like. Further change in the refractive index of the medium in the same direction causes the fringes to reappear and gradually intensify as the refractive index differs more and more from that of the film. In practice, however, the fringes remain invisible over a short range of variation of the medium rather than at a particular sharp value of refractive index. This is because the observer's eyes have a finite threshold sensitivity, and cease to detect the fringes when the contrast between adjacent bright and dark bands falls below this threshold. Thin S o l i d F i l m s -
Elsevier Publishing Company, Amsterdam - Printed in the Netherlands
132
A . M . KAUFFMAN
In the schematic graph (Fig. 1), the fringes vanish when the refraction of the medium/An equals /AL, and reappear when ~tm becomes/AH- A is the range of/Am in which the fringes are invisible and will vary somewhat for different observers although is remarkably constant for any particular observer. The refractive index of the film is/A, and when/An = /A, the fringe intensity I = 0 since the surface of the film is optically speaking non-existent at the wavelength used.
Fringe l intensity I
Observer's-
threshold
0
--
index of medium ~m Refroctive
Fig. 1.
The observer therefore attempts to find/AL and PI~ as accurately as possible and calculates # from these. It can be shown from Fresnel's formula that, in fact,/A is the geometric mean of/AL and [An (see Appendix).
EXPERIMENT TO FIND THE REFRACTIVE INDEX OF A THIN SILICA FILM DEPOSITED ON A SILICON WAFER
The wafer was about 2 x 0.5 cm coated with a thermally grown oxide layer about 0.5 micron thick. The regularity of the film thickness was such that no fringes could be seen by light reflected offthe air/SiO2 and SiO2/Si interfaces; some were therefore produced by briefly dipping the end of the wafer in hydrofluoric acid to dissolve some of the SiO2 away leaving an irregular ramp, which in diffused sodium light exhibited intense fringes. The source consisted of a sodium vapour lamp placed behind a white translucent 10" x 8" perspex sheet which acted as the diffuser. The wafer was placed in a small beaker, covered with about 5 ml of benzene, and viewed with the naked eye, approximately normally, in reflected sodium light. The refractive index of benzene is about 1.50 and that of SiO2 about 1.47. Thus the fringes were at this stage visible, but not nearly as intense as before immersion.
REFRACTIVE INDEX OF THIN SILICA FILMS
133
Several drops of acetone (index 1.36) were added to the beaker and well mixed in by swirling. This slight lowering of the refractive index of the medium caused some fading of the fringes on the wafer. Further portions of acetone were added, the fringes becoming progressively fainter until all but invisible. Adding small portions of acetone the index of the medium was gradually lowered into the A-region when the fringes disappeared completely, their intensity having fallen below the threshold of observation. The additions were carefully continued until the fringes just reappeared. At this stage a sample of the medium (at the PL point) was withdrawn and labelled " L t " (i.e. the/t L value for run number I). The procedure was repeated in the reverse direction, i.e. drops of benzene were added to the wafer initially immersed in acetone till the fringes first disappeared and then just reappeared, a sample being then withdrawn and labelled "H~" (the #n value for run number 1). The point of taking a sample when the fringes are just reappearing rather than just disappearing is to avoid errors due to after-image effects, when the observer continues to see the fringes he has been peering at a little after they have in fact fallen below his visual threshold. Three more runs were similarly made to obtain samples L2, H2, L3, H3, and L4, H4, and their refractive indices were measured using an Abbd refractometer, calibrated at the sodium D-lines (5890 A). The results obtained are in Table I. TABLE I REFRACTOMETER READINGS
Run
ttL
I~H
I 2 3 4
1.4558 1.4561 1.4564 1.4576
1.4755 1.4750 1.4756 1.4771
M eans
#L 1.4564
~H 1.4758
•"./* = ( ~ L ~ H = 1.4661-k~
The refractive index of the film was calculated as # = X/~LPH = X/1.~.-.-.-.-.-.-.-.-~4 X 1.4758 = 1.4661 __+0.0003 where 0.0003 is the standard error, calculated as in Table II.
DISCUSSION
Errors It is true that threshold values are subjective, and will vary from observer to observer. The present experiment, however, is designed to convert this personal Thin Solid Films, 1 (1967) 131-136
134 TABLE
A.M.
KAUFFMAN
II
CALCULATION OF THE STANDARD ERROR~ ~t
Run
d L x 10 - a
1 2
6 3
dL 2 × 10 -8 36 9
3
0
0
4
12
144
d n X 10 -4
dn2 × 10 -8
1 2 3
3 8 2
9 64 4
4
13
169
~ ' d 2 × 10 - s cr
where d = difference between reading and mean ~r = s t a n d a r d d e v i a t i o n
/z~d 2 ----~J n ~ = standard error a = ~ ~/n n = total number of readings = 8 .', # = 1.4661 ± 0 . 0 0 0 3
435 7.4 x 10 -4 ~ 3 x 10 - a
error into a random error, which is then statistically accounted for with the rest of the random errors. It does this in the following way. Several observers with different visual thresholds will each obtain a different pair of/~ L and #n values. The observer with the most sensitive eyes i.e. the lowest threshold, will obtain the least difference between his #L and #n pair. But, as can be seen from the calculation given in the appendix, the refractive index of the film equals the geometric mean of any pair of/~L and #H values, provided both values are recorded at the same intensity level. And they will be at the same intensity level if the observer's threshold has not altered during the one or two minutes taken to obtain one pair of readings, an assumption borne out by the very low standard errors calculated for this method. Thus on taking the geometric mean of his own personal pair of/~L and #H values, each observer arrives at the same value of refractive index, subject only to the usual (calculable) random and (unknown) systematic errors. Despite the fact that the determination depends on visual threshold judge-
TABLE
III
SOME RESULTS FOR VARIOUS SiO2 SAMPLES
Film
# Present method
Other values*
P y r o l y t i c SiO~ o n G a A s
1.4464±0.0001 1 . 4 4 9 4 ~z0.0003
1.44-1.45
T h e r m a l SiO2 o n Si grown by various techniques
1.4642i0.0001 1.4661 ± 0 . 0 0 0 3 1.46325z 0.0002 1.4673 ~ 0 . 0 0 0 1
1.462
* W . A . PLISKIN, d. Eleetrochem. Soc., 112 (1965) 1 0 1 3 - 1 0 1 9 .
REFRACTIVE INDEX OF THIN SILICA FILMS
135
ments, the very low (0.0002 typically) standard errors obtained show that the method is precise. Greater precision can be obtained by simply taking more pairs of readings, though an error of _ 0.0003, obtained from four pairs, was sufficient for the purposes of the experiment described above. Systematic errors, such as in the calibration of the refractometer, or in the theory of the method, might be estimated by comparing results obtained for a particular film using this and other methods. This has not been attempted but results in general compare quite well with some values found by others for similar films (see Table III).
Preparation of the film The determination is essentially a destructive one, since a ramp or abrupt irregularity must be produced in the film (unless it is already sufficiently irregular) to provide well-contrasted interference fringes. A parallel-sided film, of course, exhibits no fringes but rather a uniform tint. The exact shape of the irregularity, and hence of the fringes, does not in the least matter. Dipping the edge of the silica film in hydrofluoric acid produces the necessary irregularities and consequent fringes, which may for the purposes of the determination be circles, stripes or whatever. A less destructive technique is to etch a step across the film, using photolithography or a similarly controlled procedure. The step is formed near the edge of the film leaving most of it intact and useable. Under the conditions of the determination the step appears to the naked eye as a sharp dark line, which vanishes at the/t-points. If the film is too thin to show any discrete fringes, i.e. less than 2/4 thick (neglecting phase-changes on reflection) the step technique may still be used. In this case the step appears as a boundary between two areas of different brightness, since the amount of light reflected depends on the extent of interference and thus the film thickness. This brightness-boundary is, however, not as distinct as are true fringes, and several more readings are usually needed to obtain similar accuracy.
APPLICABILITY OF THE METHOD
This simple method can only be used to find refractive indices at wavelengths within the visible spectrum (by using various vapour lamps besides sodium) and with a film whose index lies between those of two suitable liquids. "Suitable" here means miscible, inert to the film, and not unduly noxious to work with. In practice the limits are about 1.3 (water) to about 2.2 (mercuric iodide in aniline). Moreover, the film on the substrate should, when appropriately etched, Thin Solid Films, 1 (1967) 131-136
136
A.M. KAUFFMAN
show good fringes in air. An opaque reflecting substrate best achieves this, but if a transparent substrate is used its refractive index should differ as much as possible from that of the film. The author has applied the present method to silicon dioxide films on gallium arsenide and on silicon substrates, which are both opaque.
ACKNOWLEDGEMENTS The author wishes to thank Dr. E. R. Skelt, Mr. P. R. Wilson, and Mr. W. R. MacEwan for supplying the samples used in the experiments.
APPENDIX
Fresnel's formula gives the intensity of surface reflectance of a substance of index # immersed in a medium of index of #m as R~ (~t-~t~/2 at normal incidence. \ ~ + Pro/
Assume that when the fringes just become visible at #L and at/~., the reflectances of the interface are the same in both cases.
whence p = ~/~L#t~ which is the result used in the experiment.
R E F R A C T I V E INDEX OF T H I N SILICA FILMS A. M. KAUFFMAN
Central Research Laboratory, Associated Electrical Industries Limited, Rugby, Warwickshire (Gt. Britain) (Received January 24, 1967; revised March 20, 1967)
SUMMARY
A simple and precise method is described for finding the refractive index of certain thin films using a novel immersion technique.
INTRODUCTION
When a transparent isotropic solid is immersed in a liquid, reflection and refraction at the surface of the solid in general lessen, and indeed cease completely in the special case when the refractive index of the liquid equals that of the solid. If the solid is a thin interference film, the intensity of the fringe pattern diminishes on immersion, vanishing entirely in the special case, since its formation depends on reflection at the solid-liquid boundary. This fringe disappearance phenomenon is exploited in the present method, which gives quite precise results using rudimentary apparatus. In outline the method is as follows. The film, deposited on a substrate, is immersed in a liquid medium and suitable fringes are observed in monochromatic light with the unaided eye. The refractive index of the medium is gradually altered h~ s i t u by mixing in drops of another liquid until the fringes, which have been progressively fading owing to reduced interfacial reflections, vanish altogether. At this point the refractive index of the medium ideally equals that of the film and can be measured easily, using an Abb6 refractometer or the like. Further change in the refractive index of the medium in the same direction causes the fringes to reappear and gradually intensify as the refractive index differs more and more from that of the film. In practice, however, the fringes remain invisible over a short range of variation of the medium rather than at a particular sharp value of refractive index. This is because the observer's eyes have a finite threshold sensitivity, and cease to detect the fringes when the contrast between adjacent bright and dark bands falls below this threshold. Thin S o l i d F i l m s -
Elsevier Publishing Company, Amsterdam - Printed in the Netherlands
132
A . M . KAUFFMAN
In the schematic graph (Fig. 1), the fringes vanish when the refraction of the medium/An equals /AL, and reappear when ~tm becomes/AH- A is the range of/Am in which the fringes are invisible and will vary somewhat for different observers although is remarkably constant for any particular observer. The refractive index of the film is/A, and when/An = /A, the fringe intensity I = 0 since the surface of the film is optically speaking non-existent at the wavelength used.
Fringe l intensity I
Observer's-
threshold
0
--
index of medium ~m Refroctive
Fig. 1.
The observer therefore attempts to find/AL and PI~ as accurately as possible and calculates # from these. It can be shown from Fresnel's formula that, in fact,/A is the geometric mean of/AL and [An (see Appendix).
EXPERIMENT TO FIND THE REFRACTIVE INDEX OF A THIN SILICA FILM DEPOSITED ON A SILICON WAFER
The wafer was about 2 x 0.5 cm coated with a thermally grown oxide layer about 0.5 micron thick. The regularity of the film thickness was such that no fringes could be seen by light reflected offthe air/SiO2 and SiO2/Si interfaces; some were therefore produced by briefly dipping the end of the wafer in hydrofluoric acid to dissolve some of the SiO2 away leaving an irregular ramp, which in diffused sodium light exhibited intense fringes. The source consisted of a sodium vapour lamp placed behind a white translucent 10" x 8" perspex sheet which acted as the diffuser. The wafer was placed in a small beaker, covered with about 5 ml of benzene, and viewed with the naked eye, approximately normally, in reflected sodium light. The refractive index of benzene is about 1.50 and that of SiO2 about 1.47. Thus the fringes were at this stage visible, but not nearly as intense as before immersion.
REFRACTIVE INDEX OF THIN SILICA FILMS
133
Several drops of acetone (index 1.36) were added to the beaker and well mixed in by swirling. This slight lowering of the refractive index of the medium caused some fading of the fringes on the wafer. Further portions of acetone were added, the fringes becoming progressively fainter until all but invisible. Adding small portions of acetone the index of the medium was gradually lowered into the A-region when the fringes disappeared completely, their intensity having fallen below the threshold of observation. The additions were carefully continued until the fringes just reappeared. At this stage a sample of the medium (at the PL point) was withdrawn and labelled " L t " (i.e. the/t L value for run number I). The procedure was repeated in the reverse direction, i.e. drops of benzene were added to the wafer initially immersed in acetone till the fringes first disappeared and then just reappeared, a sample being then withdrawn and labelled "H~" (the #n value for run number 1). The point of taking a sample when the fringes are just reappearing rather than just disappearing is to avoid errors due to after-image effects, when the observer continues to see the fringes he has been peering at a little after they have in fact fallen below his visual threshold. Three more runs were similarly made to obtain samples L2, H2, L3, H3, and L4, H4, and their refractive indices were measured using an Abbd refractometer, calibrated at the sodium D-lines (5890 A). The results obtained are in Table I. TABLE I REFRACTOMETER READINGS
Run
ttL
I~H
I 2 3 4
1.4558 1.4561 1.4564 1.4576
1.4755 1.4750 1.4756 1.4771
M eans
#L 1.4564
~H 1.4758
•"./* = ( ~ L ~ H = 1.4661-k~
The refractive index of the film was calculated as # = X/~LPH = X/1.~.-.-.-.-.-.-.-.-~4 X 1.4758 = 1.4661 __+0.0003 where 0.0003 is the standard error, calculated as in Table II.
DISCUSSION
Errors It is true that threshold values are subjective, and will vary from observer to observer. The present experiment, however, is designed to convert this personal Thin Solid Films, 1 (1967) 131-136
134 TABLE
A.M.
KAUFFMAN
II
CALCULATION OF THE STANDARD ERROR~ ~t
Run
d L x 10 - a
1 2
6 3
dL 2 × 10 -8 36 9
3
0
0
4
12
144
d n X 10 -4
dn2 × 10 -8
1 2 3
3 8 2
9 64 4
4
13
169
~ ' d 2 × 10 - s cr
where d = difference between reading and mean ~r = s t a n d a r d d e v i a t i o n
/z~d 2 ----~J n ~ = standard error a = ~ ~/n n = total number of readings = 8 .', # = 1.4661 ± 0 . 0 0 0 3
435 7.4 x 10 -4 ~ 3 x 10 - a
error into a random error, which is then statistically accounted for with the rest of the random errors. It does this in the following way. Several observers with different visual thresholds will each obtain a different pair of/~ L and #n values. The observer with the most sensitive eyes i.e. the lowest threshold, will obtain the least difference between his #L and #n pair. But, as can be seen from the calculation given in the appendix, the refractive index of the film equals the geometric mean of any pair of/~L and #H values, provided both values are recorded at the same intensity level. And they will be at the same intensity level if the observer's threshold has not altered during the one or two minutes taken to obtain one pair of readings, an assumption borne out by the very low standard errors calculated for this method. Thus on taking the geometric mean of his own personal pair of/~L and #H values, each observer arrives at the same value of refractive index, subject only to the usual (calculable) random and (unknown) systematic errors. Despite the fact that the determination depends on visual threshold judge-
TABLE
III
SOME RESULTS FOR VARIOUS SiO2 SAMPLES
Film
# Present method
Other values*
P y r o l y t i c SiO~ o n G a A s
1.4464±0.0001 1 . 4 4 9 4 ~z0.0003
1.44-1.45
T h e r m a l SiO2 o n Si grown by various techniques
1.4642i0.0001 1.4661 ± 0 . 0 0 0 3 1.46325z 0.0002 1.4673 ~ 0 . 0 0 0 1
1.462
* W . A . PLISKIN, d. Eleetrochem. Soc., 112 (1965) 1 0 1 3 - 1 0 1 9 .
REFRACTIVE INDEX OF THIN SILICA FILMS
135
ments, the very low (0.0002 typically) standard errors obtained show that the method is precise. Greater precision can be obtained by simply taking more pairs of readings, though an error of _ 0.0003, obtained from four pairs, was sufficient for the purposes of the experiment described above. Systematic errors, such as in the calibration of the refractometer, or in the theory of the method, might be estimated by comparing results obtained for a particular film using this and other methods. This has not been attempted but results in general compare quite well with some values found by others for similar films (see Table III).
Preparation of the film The determination is essentially a destructive one, since a ramp or abrupt irregularity must be produced in the film (unless it is already sufficiently irregular) to provide well-contrasted interference fringes. A parallel-sided film, of course, exhibits no fringes but rather a uniform tint. The exact shape of the irregularity, and hence of the fringes, does not in the least matter. Dipping the edge of the silica film in hydrofluoric acid produces the necessary irregularities and consequent fringes, which may for the purposes of the determination be circles, stripes or whatever. A less destructive technique is to etch a step across the film, using photolithography or a similarly controlled procedure. The step is formed near the edge of the film leaving most of it intact and useable. Under the conditions of the determination the step appears to the naked eye as a sharp dark line, which vanishes at the/t-points. If the film is too thin to show any discrete fringes, i.e. less than 2/4 thick (neglecting phase-changes on reflection) the step technique may still be used. In this case the step appears as a boundary between two areas of different brightness, since the amount of light reflected depends on the extent of interference and thus the film thickness. This brightness-boundary is, however, not as distinct as are true fringes, and several more readings are usually needed to obtain similar accuracy.
APPLICABILITY OF THE METHOD
This simple method can only be used to find refractive indices at wavelengths within the visible spectrum (by using various vapour lamps besides sodium) and with a film whose index lies between those of two suitable liquids. "Suitable" here means miscible, inert to the film, and not unduly noxious to work with. In practice the limits are about 1.3 (water) to about 2.2 (mercuric iodide in aniline). Moreover, the film on the substrate should, when appropriately etched, Thin Solid Films, 1 (1967) 131-136
136
A.M. KAUFFMAN
show good fringes in air. An opaque reflecting substrate best achieves this, but if a transparent substrate is used its refractive index should differ as much as possible from that of the film. The author has applied the present method to silicon dioxide films on gallium arsenide and on silicon substrates, which are both opaque.
ACKNOWLEDGEMENTS The author wishes to thank Dr. E. R. Skelt, Mr. P. R. Wilson, and Mr. W. R. MacEwan for supplying the samples used in the experiments.
APPENDIX
Fresnel's formula gives the intensity of surface reflectance of a substance of index # immersed in a medium of index of #m as R~ (~t-~t~/2 at normal incidence. \ ~ + Pro/
Assume that when the fringes just become visible at #L and at/~., the reflectances of the interface are the same in both cases.
whence p = ~/~L#t~ which is the result used in the experiment.