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Fundamental reflectivity spectra of Cd3As2 thin films
Thin Soh'd Fihns, I01 (1983) 115-121
ELECTRONICS AND OPTICS
115
F U N D A M E N T A L R E F L E C T I V I T Y SPECTRA O F Cd3As 2 T H I N F I L M S KATARZYNA KARNICKA-MOSCICKA*AND ANDRZEJ KISIEL Institute q[' Physics, Jagellonian Unil:ersity, ul. Reymonta 4.30-059 Krakow (Poland)
LIDIA ZDANOWICZ Institute qf Solid State Physics, Polish Academy of Science. Zahrze (Pohmd)
(Received April 7, 1982: accepted October 19, 1982)
Fundamental reflectivity spectra of thin polycrystalline and amorphous thin Cd3As 2 films are reported. The results for polycrystalline samples can be qualitatively explained in terms of a reflecting surface roughness only. For amorphous films the most probable explanation is provided by variations in the short- and mediumrange order.
1. INTRODUCTION Cadmium arsenide (Cd3As2) is a degenerate n-type semiconductor characterized by high electron mobility with at the same time low effective mass t. It also has a small inverse energy gap of the HgTe type 2. Although Cd3As 2 always forms monocrystalline or polycrystalline samples in the bulk, it is possible to obtain amorphous samples in the form of thin films. The properties of both crystalline and amorphous forms of Cd3As 2 have been studied in recent years. In particular, the band structure of the material has been studied by photoemission and fundamental reflectance spectrometry 3 s. Most of the work was done on bulk crystalline samples 3 7 but for thin films the fundamental reflectivity R ( E ) spectrum has been measured only once and in a very narrow energy range (0.4-1.0 eV) s. In our studies R ( E ) of thin polycrystalline and amorphous Cd3As2 films was investigated in a wider energy range (0.8-5.9 eV). 2. RESULTS All the samples of thin amorphous and polycrystalline Cd3As 2 films investigated were prepared in the Institute of Solid State Physics of the Polish Academy of Science in Zabrze. The films were obtained by thermal vacuum (10 -6 Torr) deposition of Cd3As2 material onto mica or glass substrates ~. The substrate temperature T~ was stabilized and samples were prepared for various temperatures from 90 to 450 K. This allowed us to obtain amorphous ( ~ < 390 K) and * On leave at Laboratoire Maurice Letort, CNRS, route de Vandoeuvre, B.P. 104, 54600 Villersles-Nancy, France. 0040-6090/83/0000-0000/$03.00
© ElsevierSequoia/Printed in The Netherlands
116
K. KARNICKA-MOSCICKA, A. KISIEL, L. ZDANOWICZ
polycrystalline (T~ > 390 K) films with various degrees of order, grain sizes and microstructures 9'1°. The films had thicknesses ranging from 0.4 to 4 pm. The structure of the films was determined on the basis of X-ray diffraction; all amorphous films were characterized by smeared halo-type diffraction patterns• The state of the reflecting surface (microstructure) of each film was examined with electron microscopy techniques (reflection microscopy and transmission microscopy on carbon replicas). The fundamental reflectivity R(E) spectra were obtained at room temperature in the energy range from 0.8 to 5.9 eV with the reflectometer described in ref. 11. 50.
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Fig. t. Fundamentalreflectivityspectraofthin polycrystallineCd3Asz films:(a)for samples deposited at T~of 450 K (curve 1), 440 K (curve 2), 400 K (curve 3), 445 K (curve 4) and 390 K (curve 5); (b) simulated by means of the Porteus model for various surface roughnesses, assuming the experimental data to represent the spectrum from a perfectly flat surface (curve 1) and using grain sizes of 0.1 p.m (curve 2), 0.2 jam (curve 3) and 0•3 gm (curve 4).
Cd3As 2
R E F L E C T I V l T Y OF
117
Nearly normal incidence of the electromagnetic beam to the reflecting surface (within 6 °) was maintained throughout. The results are shown in Figs. l(a) and 2. The R(E) spectra for five polycrystalline thin films, each deposited at a different T~ from 390 to 450 K, are collected together in Fig. l(a). The amorphous films can be divided into two different groups. Those obtained at substrate temperatures T~ low enough (room temperature) to be well within the temperature range typical for amorphous phase formation are characterized by the type of spectrum shown in Fig. 2(b). The typical spectrum of the second group, obtained for higher Ts in the transition range of temperatures is shown in Fig. 2(a).
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Fig. 2. Fundamentalreflectivityspectrafor thin amorphous Cd~As2 films:(a) a typical sample deposited at 370 K from the transitionrangeof temperatures;(b) a sampledeposited at 293 K typical of amorphous phase formation.
1 18
K. KARNICKA-MOSCICKA, A. KISIEL, L. ZDANOWICZ
3. DISCUSSION It is obvious from Fig, l(a) that the spectrum ofa polycrystalline film deposited at the highest substrate temperature studied is characterized by the highest reflectance and richest spectral structure• The structure of the spectrum is very similar to that of the monocrystal spectrum 7. It is expected that deposition onto substrates at different temperatures can lead to the formation of films with better or worse degrees of order and different grain sizes m 1o. Crystal lattice defects causing perturbation of the band structure may in consequence lead to smearing of the spectral structure. For example, the weakening of the 3.8 eV transition in Fig. l(a) to nearly total disappearance would be caused by strong deformation of the band
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REFLECTIVITY OF C d 3 A s 2
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structure in the vicinity of the critical point responsible for this transition v. However, in interpreting the R(E) spectral variation from sample to sample we cannot neglect the influence of a reflecting surface roughness. As has been shown before ~2, the roughness may also have a significant influence on the measured reflectivity. To estimate the effect in this case, the theory of Porteus ~3 was applied. A real reflecting surface is approximated in the theory as an isotropic surface consisting of facets of random size and shape which are all aligned parallel to the mean surface-level plane and are located at random levels relative to this plane. In such an approximation the surface is characterized by two statistical parameters: the r.m.s, roughness S
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120
K. KARNICKA-MOSCICKA, A. KISIEL, L. ZDANOWICZ
describing fluctuations in the levels and the r.m.s, slope m describing fluctuations in the facets' size and shape (see ref. 14, Fig. 3). The reflecting surfaces under investigation were parametrized accordingly on the basis of the electron microscopy data. The surface of a polycrystalline film is built up from microcrystallites growing from the substrate 9' lo. We found that 0.1-0.3 ~tm was a reasonable approximation for the microcrystallite grain size, which led to 0.01 I-tm < S < 0.05 ~tm: m was chosen arbitrarily but reasonably (see refs. 13 and 14) to be 0.035 for our films. Further, because of the similarity of spectrum 1 in Fig. l(a) to those of the monocrystal 7, this spectrum was assumed to be characteristic of a perfectly flat reflecting surface. Later the spectrum was modulated by the roughness function; a detailed discussion of the procedure is given in refs. 11 and 14. Figure l(b) shows as an example the predicted spectral changes caused by different degrees of roughness typical of our samples. We notice that for increasing grain size the amplitude of the simulated spectrum for any energy E decreases and furthermore the shape of the spectrum is more strongly affected towards higher energies. A comparison of the simulated curves with experimental data shows that simulated surface roughness introduces a general smoothing out of all structures which is not entirely observed in experiments. However, the agreement would be improved 14 by an appropriate variation of the arbitrary parameter m. Thus we conclude that the main tendency in spectral variation with substrate temperature during deposition can be explained qualitatively on the basis of the properties of the reflecting surface alone. In particular, it should be kept in mind that increasing T, may improve not only the microstructure of the surface (giving a less rough surface) but also the quality of crystallinity (better band structure of the material) 9' lo. However, the extent of the surface roughness effect on the fundamental reflectivity spectrum makes it impossible to extract in any reasonable way a contribution to R(E) from a source of perturbation of the band structure, and we are therefore in favour of surface roughness as an explanation of the variation in the R(E) spectra of thin Cd3As 2 polycrystalline films studied in the present paper. The thin amorphous films of Fig. 2 are characterized by a widely smeared spectrum with a single broad peak. This type of R(E) spectrum has also been observed before 15 for the amorphous materials of groups IV and III-V. The main difference between the spectrum of the amorphous film and that ofa polycrystalline film is in the total lack of sharp characteristic structure so typical of crystalline material. This reflects the absence of singularities in the joint density of states function, i.e. the lack of long-range order within amorphous material. The position and maximum intensity of the peak vary significantly and depend on the detailed preparation conditions. With the deposition rate remaining constant, the properties are predominantly determined by the substrate temperature ~. There is a visible difference in the peak intensity and position for films deposited onto substrates at room temperature, when amorphous samples are always formed, and those for films prepared on substrates with ~ lying in the transition range of temperatures, i.e. above room temperature but below temperatures typical for the formation of polycrystalline films (Fig. 2). It must be pointed out that we found it impossible to explain the difference between the spectra on the basis of surface roughness variations, as was possible for polycrystalline samples. Unlike for polycrystalline films, the surfaces of amorphous
REFLECTIVITY OF C d 3 A s 2
121
films are built up from closely packed bulges more or less ellipsoidal in shape but different in size 9' to. As before, surface roughness was parametrized by means of the Porteus theory t 3,1,* and reasonable values for an average bulge size were found to be within the 0.1-0.5 lam range. The results of the simulation are shown in Fig. 3. Unlike the polycrystalline material, none of the amorphous samples was assumed to possess a "perfect" spectrum and thus with the aid of a roughness function we tried to guess the spectrum from experimental surface-roughness-disturbed spectra. Evidently (Fig. 3) roughness with the sizes observed is not able to produce, within the model, significant changes in the peak position and intensity. Thus we are rather in favour of another type of explanation for the observed differences in the spectra shown in Fig. 2. Studies of the stoichiometry of both kinds of amorphous-type sample did not show any significant deviation from the samples' average composition or furthermore any correlation between the spectrum and the composition of the film. We also noticed that all amorphous films were characterized by smeared halo-type X-ray diffraction patterns, indistinguishable from each other. In the light of these facts, it is very probable that the differences are due to the structural properties of both types of amorphous film and particularly to short- and mediumrange order. The substrate temperature dependence of the fundamental reflectivity spectrum supports such a suggestion. Because of the difficulties in the determination of the degree of order of amorphous films after preparation, a particularly careful analysis of correlations between the detailed preparation conditions and the degree of structural order is required to understand the nature of the differences. Such studies are planned for the future. ACKNOWLEDGMENT
The authors are grateful to Dr. Myron W. Evans from the University College of Wales, Aberystwyth, for his comments during preparation of the manuscript. REFERENCES 1 W. •danowicz and L. z~danowicz. Annu. ReL,. Mater. Sci., 5 (1975) 301. 2 J. Bodnar, Proe. 1st Int. Col~/~ on Narrow-Gap Semiconductors, Panstwowe Wydawnictwo Naukowe, Warsaw, 1977. 3 V.V. Sobolev, N. N. Sybru, T. A. Ziubiba and J. A. UgaL Fiz. Tekh. Poluprovodn., 5 ( 1971 ) 327. 4 M. Zivitz and J. R. Stevenson, Phys. Ret,. B, 10 (1974) 3457. 5 V.P. Bhola, Phys. Status Solidi A. 43 (1976) K 179 : J. Phys. Chem. Solids', 38 (1977) 1237. 6 M.J. A u b i n a n d J . P. Cloutier, Can. J. Phvs.,53(1975) 1642. 7 K. Karnicka-Moscicka, A. Kisiel and L. Zdanowicz, Solid State Commun., in the press. 8 L . M . Rogers, R . M . J e n k i n s a n d A . J. Crocker, J. Phys. D, 4(1971)471. 9 L. z~danowicz and S. Miotowska, Thin Solid Films, 29 (1975) 177. 10 J. Jurusik and L. z~danowicz, Thin Solid Films, 67 (1980) 285. 11 K. Karnicka-Moscicka, Ph.D. Thesis, Jagellonian University, Krakow, 1981. 12 1. Ohlidal and K. Navrfitil, Thin Solid Films, 31 (1976) 223. 13 J.O. Porteus, J. Opt. Soe. Am., 53 (1963) 1394. 14 K. Karnicka-Moscicka and A. Kisiel, Sur]~ Sei., 121 (1982) L545. 15 M . L . Th~ye, in F. Abel6s (ed.), Optical Properties q/Solids, North-Holland, Amsterdam, 1976.
ELECTRONICS AND OPTICS
115
F U N D A M E N T A L R E F L E C T I V I T Y SPECTRA O F Cd3As 2 T H I N F I L M S KATARZYNA KARNICKA-MOSCICKA*AND ANDRZEJ KISIEL Institute q[' Physics, Jagellonian Unil:ersity, ul. Reymonta 4.30-059 Krakow (Poland)
LIDIA ZDANOWICZ Institute qf Solid State Physics, Polish Academy of Science. Zahrze (Pohmd)
(Received April 7, 1982: accepted October 19, 1982)
Fundamental reflectivity spectra of thin polycrystalline and amorphous thin Cd3As 2 films are reported. The results for polycrystalline samples can be qualitatively explained in terms of a reflecting surface roughness only. For amorphous films the most probable explanation is provided by variations in the short- and mediumrange order.
1. INTRODUCTION Cadmium arsenide (Cd3As2) is a degenerate n-type semiconductor characterized by high electron mobility with at the same time low effective mass t. It also has a small inverse energy gap of the HgTe type 2. Although Cd3As 2 always forms monocrystalline or polycrystalline samples in the bulk, it is possible to obtain amorphous samples in the form of thin films. The properties of both crystalline and amorphous forms of Cd3As 2 have been studied in recent years. In particular, the band structure of the material has been studied by photoemission and fundamental reflectance spectrometry 3 s. Most of the work was done on bulk crystalline samples 3 7 but for thin films the fundamental reflectivity R ( E ) spectrum has been measured only once and in a very narrow energy range (0.4-1.0 eV) s. In our studies R ( E ) of thin polycrystalline and amorphous Cd3As2 films was investigated in a wider energy range (0.8-5.9 eV). 2. RESULTS All the samples of thin amorphous and polycrystalline Cd3As 2 films investigated were prepared in the Institute of Solid State Physics of the Polish Academy of Science in Zabrze. The films were obtained by thermal vacuum (10 -6 Torr) deposition of Cd3As2 material onto mica or glass substrates ~. The substrate temperature T~ was stabilized and samples were prepared for various temperatures from 90 to 450 K. This allowed us to obtain amorphous ( ~ < 390 K) and * On leave at Laboratoire Maurice Letort, CNRS, route de Vandoeuvre, B.P. 104, 54600 Villersles-Nancy, France. 0040-6090/83/0000-0000/$03.00
© ElsevierSequoia/Printed in The Netherlands
116
K. KARNICKA-MOSCICKA, A. KISIEL, L. ZDANOWICZ
polycrystalline (T~ > 390 K) films with various degrees of order, grain sizes and microstructures 9'1°. The films had thicknesses ranging from 0.4 to 4 pm. The structure of the films was determined on the basis of X-ray diffraction; all amorphous films were characterized by smeared halo-type diffraction patterns• The state of the reflecting surface (microstructure) of each film was examined with electron microscopy techniques (reflection microscopy and transmission microscopy on carbon replicas). The fundamental reflectivity R(E) spectra were obtained at room temperature in the energy range from 0.8 to 5.9 eV with the reflectometer described in ref. 11. 50.
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Fig. t. Fundamentalreflectivityspectraofthin polycrystallineCd3Asz films:(a)for samples deposited at T~of 450 K (curve 1), 440 K (curve 2), 400 K (curve 3), 445 K (curve 4) and 390 K (curve 5); (b) simulated by means of the Porteus model for various surface roughnesses, assuming the experimental data to represent the spectrum from a perfectly flat surface (curve 1) and using grain sizes of 0.1 p.m (curve 2), 0.2 jam (curve 3) and 0•3 gm (curve 4).
Cd3As 2
R E F L E C T I V l T Y OF
117
Nearly normal incidence of the electromagnetic beam to the reflecting surface (within 6 °) was maintained throughout. The results are shown in Figs. l(a) and 2. The R(E) spectra for five polycrystalline thin films, each deposited at a different T~ from 390 to 450 K, are collected together in Fig. l(a). The amorphous films can be divided into two different groups. Those obtained at substrate temperatures T~ low enough (room temperature) to be well within the temperature range typical for amorphous phase formation are characterized by the type of spectrum shown in Fig. 2(b). The typical spectrum of the second group, obtained for higher Ts in the transition range of temperatures is shown in Fig. 2(a).
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Fig. 2. Fundamentalreflectivityspectrafor thin amorphous Cd~As2 films:(a) a typical sample deposited at 370 K from the transitionrangeof temperatures;(b) a sampledeposited at 293 K typical of amorphous phase formation.
1 18
K. KARNICKA-MOSCICKA, A. KISIEL, L. ZDANOWICZ
3. DISCUSSION It is obvious from Fig, l(a) that the spectrum ofa polycrystalline film deposited at the highest substrate temperature studied is characterized by the highest reflectance and richest spectral structure• The structure of the spectrum is very similar to that of the monocrystal spectrum 7. It is expected that deposition onto substrates at different temperatures can lead to the formation of films with better or worse degrees of order and different grain sizes m 1o. Crystal lattice defects causing perturbation of the band structure may in consequence lead to smearing of the spectral structure. For example, the weakening of the 3.8 eV transition in Fig. l(a) to nearly total disappearance would be caused by strong deformation of the band
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REFLECTIVITY OF C d 3 A s 2
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structure in the vicinity of the critical point responsible for this transition v. However, in interpreting the R(E) spectral variation from sample to sample we cannot neglect the influence of a reflecting surface roughness. As has been shown before ~2, the roughness may also have a significant influence on the measured reflectivity. To estimate the effect in this case, the theory of Porteus ~3 was applied. A real reflecting surface is approximated in the theory as an isotropic surface consisting of facets of random size and shape which are all aligned parallel to the mean surface-level plane and are located at random levels relative to this plane. In such an approximation the surface is characterized by two statistical parameters: the r.m.s, roughness S
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E E e V ] * I0 (b') Fig. 3. Comparison of the experimental spectra of thin amorphous Cd3As 2 films from Fig. 2 {...) with simulated spectra for average bulge sizes of 0.5 pm (curves 1) and 0.1 p.m (curves 2) and for two variations of the Porteus model ([a), (b) and (a'), (b') respectively).
120
K. KARNICKA-MOSCICKA, A. KISIEL, L. ZDANOWICZ
describing fluctuations in the levels and the r.m.s, slope m describing fluctuations in the facets' size and shape (see ref. 14, Fig. 3). The reflecting surfaces under investigation were parametrized accordingly on the basis of the electron microscopy data. The surface of a polycrystalline film is built up from microcrystallites growing from the substrate 9' lo. We found that 0.1-0.3 ~tm was a reasonable approximation for the microcrystallite grain size, which led to 0.01 I-tm < S < 0.05 ~tm: m was chosen arbitrarily but reasonably (see refs. 13 and 14) to be 0.035 for our films. Further, because of the similarity of spectrum 1 in Fig. l(a) to those of the monocrystal 7, this spectrum was assumed to be characteristic of a perfectly flat reflecting surface. Later the spectrum was modulated by the roughness function; a detailed discussion of the procedure is given in refs. 11 and 14. Figure l(b) shows as an example the predicted spectral changes caused by different degrees of roughness typical of our samples. We notice that for increasing grain size the amplitude of the simulated spectrum for any energy E decreases and furthermore the shape of the spectrum is more strongly affected towards higher energies. A comparison of the simulated curves with experimental data shows that simulated surface roughness introduces a general smoothing out of all structures which is not entirely observed in experiments. However, the agreement would be improved 14 by an appropriate variation of the arbitrary parameter m. Thus we conclude that the main tendency in spectral variation with substrate temperature during deposition can be explained qualitatively on the basis of the properties of the reflecting surface alone. In particular, it should be kept in mind that increasing T, may improve not only the microstructure of the surface (giving a less rough surface) but also the quality of crystallinity (better band structure of the material) 9' lo. However, the extent of the surface roughness effect on the fundamental reflectivity spectrum makes it impossible to extract in any reasonable way a contribution to R(E) from a source of perturbation of the band structure, and we are therefore in favour of surface roughness as an explanation of the variation in the R(E) spectra of thin Cd3As 2 polycrystalline films studied in the present paper. The thin amorphous films of Fig. 2 are characterized by a widely smeared spectrum with a single broad peak. This type of R(E) spectrum has also been observed before 15 for the amorphous materials of groups IV and III-V. The main difference between the spectrum of the amorphous film and that ofa polycrystalline film is in the total lack of sharp characteristic structure so typical of crystalline material. This reflects the absence of singularities in the joint density of states function, i.e. the lack of long-range order within amorphous material. The position and maximum intensity of the peak vary significantly and depend on the detailed preparation conditions. With the deposition rate remaining constant, the properties are predominantly determined by the substrate temperature ~. There is a visible difference in the peak intensity and position for films deposited onto substrates at room temperature, when amorphous samples are always formed, and those for films prepared on substrates with ~ lying in the transition range of temperatures, i.e. above room temperature but below temperatures typical for the formation of polycrystalline films (Fig. 2). It must be pointed out that we found it impossible to explain the difference between the spectra on the basis of surface roughness variations, as was possible for polycrystalline samples. Unlike for polycrystalline films, the surfaces of amorphous
REFLECTIVITY OF C d 3 A s 2
121
films are built up from closely packed bulges more or less ellipsoidal in shape but different in size 9' to. As before, surface roughness was parametrized by means of the Porteus theory t 3,1,* and reasonable values for an average bulge size were found to be within the 0.1-0.5 lam range. The results of the simulation are shown in Fig. 3. Unlike the polycrystalline material, none of the amorphous samples was assumed to possess a "perfect" spectrum and thus with the aid of a roughness function we tried to guess the spectrum from experimental surface-roughness-disturbed spectra. Evidently (Fig. 3) roughness with the sizes observed is not able to produce, within the model, significant changes in the peak position and intensity. Thus we are rather in favour of another type of explanation for the observed differences in the spectra shown in Fig. 2. Studies of the stoichiometry of both kinds of amorphous-type sample did not show any significant deviation from the samples' average composition or furthermore any correlation between the spectrum and the composition of the film. We also noticed that all amorphous films were characterized by smeared halo-type X-ray diffraction patterns, indistinguishable from each other. In the light of these facts, it is very probable that the differences are due to the structural properties of both types of amorphous film and particularly to short- and mediumrange order. The substrate temperature dependence of the fundamental reflectivity spectrum supports such a suggestion. Because of the difficulties in the determination of the degree of order of amorphous films after preparation, a particularly careful analysis of correlations between the detailed preparation conditions and the degree of structural order is required to understand the nature of the differences. Such studies are planned for the future. ACKNOWLEDGMENT
The authors are grateful to Dr. Myron W. Evans from the University College of Wales, Aberystwyth, for his comments during preparation of the manuscript. REFERENCES 1 W. •danowicz and L. z~danowicz. Annu. ReL,. Mater. Sci., 5 (1975) 301. 2 J. Bodnar, Proe. 1st Int. Col~/~ on Narrow-Gap Semiconductors, Panstwowe Wydawnictwo Naukowe, Warsaw, 1977. 3 V.V. Sobolev, N. N. Sybru, T. A. Ziubiba and J. A. UgaL Fiz. Tekh. Poluprovodn., 5 ( 1971 ) 327. 4 M. Zivitz and J. R. Stevenson, Phys. Ret,. B, 10 (1974) 3457. 5 V.P. Bhola, Phys. Status Solidi A. 43 (1976) K 179 : J. Phys. Chem. Solids', 38 (1977) 1237. 6 M.J. A u b i n a n d J . P. Cloutier, Can. J. Phvs.,53(1975) 1642. 7 K. Karnicka-Moscicka, A. Kisiel and L. Zdanowicz, Solid State Commun., in the press. 8 L . M . Rogers, R . M . J e n k i n s a n d A . J. Crocker, J. Phys. D, 4(1971)471. 9 L. z~danowicz and S. Miotowska, Thin Solid Films, 29 (1975) 177. 10 J. Jurusik and L. z~danowicz, Thin Solid Films, 67 (1980) 285. 11 K. Karnicka-Moscicka, Ph.D. Thesis, Jagellonian University, Krakow, 1981. 12 1. Ohlidal and K. Navrfitil, Thin Solid Films, 31 (1976) 223. 13 J.O. Porteus, J. Opt. Soe. Am., 53 (1963) 1394. 14 K. Karnicka-Moscicka and A. Kisiel, Sur]~ Sei., 121 (1982) L545. 15 M . L . Th~ye, in F. Abel6s (ed.), Optical Properties q/Solids, North-Holland, Amsterdam, 1976.