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Antireflection properties of thermally grown silicon oxide on silicon optical elements
Infrared Physic% Vol. 7. pp. 117-l 19. Pergttmon Press Ltd. 1967. Printed in Great Britain
ANTIREFLECTION SILICON
OXIDE
PROPERTIES ON SILICON M.
OF THERMALLY OPTICAL
GROWN
ELEMENTS
MILER
Institute of Radio Engineering and Electronics Czechoslovak Academy of Sciences, Prague, Czechoslovakia (Received
2 January
1967)
Abstract-Advantageous antireflection properties of thermally grown silicon oxide on the silicon optical elements for the near infrared region, are presented. The transmissivity can be increased from 54 to 86 per cent. Due to the ease of preparation, these layers should be widely applicable.
INTRODUCTION
silicon is often used as a suitable optical material for the infrared region. In practical thicknesses silicon is transparent to infrared radiation in the region l-215 pm and has suitable mechanical and thermal properties. However, it has also a high index of refraction n = 3.4, which allows one to design lenses with a great relative aperture(tB 2) on one hand, but, on the other hand, it also brings big losses due to the high reflectivity R = 30 per cent. The high reflectivity can be removed by antireflection layers, mostly vacuum evaporated. For simple layers a quarter wave layer of silicon oxide is used(s) which can almost entirely suppress the reflection, or ZnS, which at about 10 pm increases the transmissivity for up to 30 per cent. For the more perfect antireflection properties double and triple layers are described+6). One can often apply lower requirements to the antireflection properties of those layers the manufacture of which would be technologically easier, especially at the infrared windows. One of these possibilities is the thermally grown silicon oxide which is further described. SINGLEcrystalline
EXPERIMENTAL
As is already known, a layer of silicon oxide(7) is formed on the silicon surface due to its thermal oxidation. This system Si-SiOs, may then serve as a part of thin film devices, e.g. MOS transistors. In addition, it became evident that the thermally grown SiOs has suitable antireflection properties. The silicon wafer has been subjected to the thermal oxidation on both the surfaces under the same conditions. Thus we can consider that on both the surfaces, SiOs layers of practically the same thickness were formed (Fig. 1). The system has been chosen in such a way to grow the X/Clayer with the first maximum between 2-2.5 pm, i.e. thickness of about O-38pm. The transmissivity of the whole system was measured by using the infrared spectrometer UR-10. Samples with chemically etched silicon surfaces had transmissivity according to 117
M.
MILER
si
sio>
Sic17
rT
4 /
R12
R,,
\
Reff
Reff -
/
l-l’
n 5
FIG. 1. Scheme of the:SiOs-Si-,502
100
2
I
3
system.
X Iv) .G
5
6
FIG. 2. Traosmissivity of the silicon wafer (curve b) and of the system (h/4) SiOz-Si-(h/4) silicon base chemically worked (curve a) and with the not worked one (curve c). o o o theoretical values.
7
8970
SiOz with the
Fig. 2, curve a. Transmissivity maximum reaches over 86 per cent at the wavelength 2.2 pm approx. Un-etched samples (curve c) had worse transmissivity than that of the silicon wafer only (curve b). THEORETICAL
The non-absorbing silicon wafer with thin films of non-absorbing silicon oxide on its surfaces (Fig. 1) can be considered as an optically thick layer with effective reflectivities. Transmissivity of such a system is given by the relation 1 - Rert T=-------
1 + Rerr
(1)
Antireflection
properties of thermally gown silicon oxide
119
For the effective reflectivity of the boundary,
Rett =
RLZ +
R23 + 2v”(Ri2
1 + Rl2 R23 + 2t/(Rr2
R23) co3 x R23) COS x
(2)
where Ris = (n - 1)2/(n + 1)s is the reflectivity of silicon oxide against air, and R23 = (n’ - n)s/(n’ f n)e is that against the silicon base. The argument of the cosine is x = 4rndjh, where n is the index of refraction, d the thickness of oxide layer and X is the wavelength. n’ is the refractive index of silicon. Substituting (2) into (1) we obtain T = (1 -
R12) (1 -
R23)
(1 + RIZ) (1 + R23) + &/(RlZ
R23) CO3 X’
The thickness of silicon oxide layer was determined from the first maximum of reflectivity d = h,,&4n = 0.378 pm. Using the refractive index values for the bulk amorphous silicon oxide and single crystalline silicon, achieved by the interpolation from@), the transmissivity according to (3) was calculated and the curve plotted in Fig. 2 has been obtained. It is seen that the theoreticai and experimental values are in agreement within 2 per cent. In the region 2-3.5 pm the theoretical values are higher, over 3.5 pm they are lower. Thus it is evident that the layer of silicon oxide of the mentioned thickness performed by the thermal oxidation behaves similarly as the bulk sample, regarding the refractive index in the non-absorbing region. CONCLUSION
By means of the thermal oxidation of the surfaces of silicon elements of infrared optical devices their transmissivity in near infrared can be increased by up to 30 per cent. The silicon surface must be prepared by chemical etching. The layer is mechanically and thermally very resistant and firmly connected to the base. .4&zuwlcrCpement-The author is indebted to Mr. 1. Nifevka and Mr. J. Berger from the same Institute for kindly preparing the respective samples.
I. 2. 3. 4. 5. 6. 7. 8.
REFERENCES BRIM%, H. B.. Phy~ Rev. 77, 287 (1950). TRETING.J., J. opt. Sm. Am. 41,454 (1951). Cox, J. T. and G. Hm, J. opt. Sot. Am. 48 677 (1958). HASS,G. and A. TURNER,Ergebnisse der ~oc~akuum~ec~ik tazd der Physik difnner Schichten. Vcrlagsgcs. (1957). HEAVENS,0. S., Optical Properties ofThin Solid Films. Butterworth (1955). BAUMEJRER,P. W., Hana%aok of Opticof Design, Chapter 20. U.S. Govt. Printing Office (1963). LIGENZA,J. R. and W. G. SPITZER.J. Phys. Chem. Solkfs 14,131 (1960). LANDOLT-M~NSTEIN,Zahlenwerte und Funktionen, Vol 2, Part 8, Optfsche Komtanten. Springer-Vcrlag (1962).
ANTIREFLECTION SILICON
OXIDE
PROPERTIES ON SILICON M.
OF THERMALLY OPTICAL
GROWN
ELEMENTS
MILER
Institute of Radio Engineering and Electronics Czechoslovak Academy of Sciences, Prague, Czechoslovakia (Received
2 January
1967)
Abstract-Advantageous antireflection properties of thermally grown silicon oxide on the silicon optical elements for the near infrared region, are presented. The transmissivity can be increased from 54 to 86 per cent. Due to the ease of preparation, these layers should be widely applicable.
INTRODUCTION
silicon is often used as a suitable optical material for the infrared region. In practical thicknesses silicon is transparent to infrared radiation in the region l-215 pm and has suitable mechanical and thermal properties. However, it has also a high index of refraction n = 3.4, which allows one to design lenses with a great relative aperture(tB 2) on one hand, but, on the other hand, it also brings big losses due to the high reflectivity R = 30 per cent. The high reflectivity can be removed by antireflection layers, mostly vacuum evaporated. For simple layers a quarter wave layer of silicon oxide is used(s) which can almost entirely suppress the reflection, or ZnS, which at about 10 pm increases the transmissivity for up to 30 per cent. For the more perfect antireflection properties double and triple layers are described+6). One can often apply lower requirements to the antireflection properties of those layers the manufacture of which would be technologically easier, especially at the infrared windows. One of these possibilities is the thermally grown silicon oxide which is further described. SINGLEcrystalline
EXPERIMENTAL
As is already known, a layer of silicon oxide(7) is formed on the silicon surface due to its thermal oxidation. This system Si-SiOs, may then serve as a part of thin film devices, e.g. MOS transistors. In addition, it became evident that the thermally grown SiOs has suitable antireflection properties. The silicon wafer has been subjected to the thermal oxidation on both the surfaces under the same conditions. Thus we can consider that on both the surfaces, SiOs layers of practically the same thickness were formed (Fig. 1). The system has been chosen in such a way to grow the X/Clayer with the first maximum between 2-2.5 pm, i.e. thickness of about O-38pm. The transmissivity of the whole system was measured by using the infrared spectrometer UR-10. Samples with chemically etched silicon surfaces had transmissivity according to 117
M.
MILER
si
sio>
Sic17
rT
4 /
R12
R,,
\
Reff
Reff -
/
l-l’
n 5
FIG. 1. Scheme of the:SiOs-Si-,502
100
2
I
3
system.
X Iv) .G
5
6
FIG. 2. Traosmissivity of the silicon wafer (curve b) and of the system (h/4) SiOz-Si-(h/4) silicon base chemically worked (curve a) and with the not worked one (curve c). o o o theoretical values.
7
8970
SiOz with the
Fig. 2, curve a. Transmissivity maximum reaches over 86 per cent at the wavelength 2.2 pm approx. Un-etched samples (curve c) had worse transmissivity than that of the silicon wafer only (curve b). THEORETICAL
The non-absorbing silicon wafer with thin films of non-absorbing silicon oxide on its surfaces (Fig. 1) can be considered as an optically thick layer with effective reflectivities. Transmissivity of such a system is given by the relation 1 - Rert T=-------
1 + Rerr
(1)
Antireflection
properties of thermally gown silicon oxide
119
For the effective reflectivity of the boundary,
Rett =
RLZ +
R23 + 2v”(Ri2
1 + Rl2 R23 + 2t/(Rr2
R23) co3 x R23) COS x
(2)
where Ris = (n - 1)2/(n + 1)s is the reflectivity of silicon oxide against air, and R23 = (n’ - n)s/(n’ f n)e is that against the silicon base. The argument of the cosine is x = 4rndjh, where n is the index of refraction, d the thickness of oxide layer and X is the wavelength. n’ is the refractive index of silicon. Substituting (2) into (1) we obtain T = (1 -
R12) (1 -
R23)
(1 + RIZ) (1 + R23) + &/(RlZ
R23) CO3 X’
The thickness of silicon oxide layer was determined from the first maximum of reflectivity d = h,,&4n = 0.378 pm. Using the refractive index values for the bulk amorphous silicon oxide and single crystalline silicon, achieved by the interpolation from@), the transmissivity according to (3) was calculated and the curve plotted in Fig. 2 has been obtained. It is seen that the theoreticai and experimental values are in agreement within 2 per cent. In the region 2-3.5 pm the theoretical values are higher, over 3.5 pm they are lower. Thus it is evident that the layer of silicon oxide of the mentioned thickness performed by the thermal oxidation behaves similarly as the bulk sample, regarding the refractive index in the non-absorbing region. CONCLUSION
By means of the thermal oxidation of the surfaces of silicon elements of infrared optical devices their transmissivity in near infrared can be increased by up to 30 per cent. The silicon surface must be prepared by chemical etching. The layer is mechanically and thermally very resistant and firmly connected to the base. .4&zuwlcrCpement-The author is indebted to Mr. 1. Nifevka and Mr. J. Berger from the same Institute for kindly preparing the respective samples.
I. 2. 3. 4. 5. 6. 7. 8.
REFERENCES BRIM%, H. B.. Phy~ Rev. 77, 287 (1950). TRETING.J., J. opt. Sm. Am. 41,454 (1951). Cox, J. T. and G. Hm, J. opt. Sot. Am. 48 677 (1958). HASS,G. and A. TURNER,Ergebnisse der ~oc~akuum~ec~ik tazd der Physik difnner Schichten. Vcrlagsgcs. (1957). HEAVENS,0. S., Optical Properties ofThin Solid Films. Butterworth (1955). BAUMEJRER,P. W., Hana%aok of Opticof Design, Chapter 20. U.S. Govt. Printing Office (1963). LIGENZA,J. R. and W. G. SPITZER.J. Phys. Chem. Solkfs 14,131 (1960). LANDOLT-M~NSTEIN,Zahlenwerte und Funktionen, Vol 2, Part 8, Optfsche Komtanten. Springer-Vcrlag (1962).