SOLID-STATE SPECTROSCOPY

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1 Optics and Spectroscopy Vol. 98 No pp Translated from Optika i Spektroskopiya Vol. 98 No pp Original Russian Tet Copyright 005 by Moskovskiœ. SOLID-STATE SPECTROSCOPY Transmission and Reflection of Light by Thin Semiconductor Plates in the Ecitonic Spectral Range in the Presence of Spatial Dispersion and Surface Eciton-Free Layers S. B. Moskovskiœ Ushinsky Yaroslavl State Pedagogical University Yaroslavl Russia Received June Abstract Epressions are obtained for the comple amplitude transmittance and reflectance of plane-parallel crystal plates in the ecitonic spectral range under conditions when additional polaritonic waves associated with the effect of spatial dispersion are ecited and when the presence of eciton-free layers on the surfaces of the crystal and multiple reflections in each of the layers is taken into account for different geometries of oblique incidence. 005 Pleiades Publishing Inc. In calculations of the transmission and interference reflection of light in thin monocrystal semiconductor plates in the ecitonic spectral range when the effect of spatial dispersion provides additional solutions of the dispersion equation (additional polaritonic waves [ 3]) one has to take into account the inhomogeneity of the eciton potential in the near-surface region [4]. This surface inhomogeneity of the eciton potential can often affect the transmission and reflection spectra. It is noteworthy that for the case of reflection this effect should be taken into account even for very thick in the limit semi-infinite crystals. The simplest model that takes into account the near-surface inhomogeneity resulting from the finite size of the eciton is the model of a dead layer with a background permittivity [5]. In this paper we present solutions of the problems of multibeam transmission and reflection of light by thin plane-parallel crystal plates in the presence of additional polaritonic waves and eciton-free layers (EFLs) on each of the surfaces at an oblique incidence of the light with different polarizations with respect to the plane of incidence and the optic ais. As the EFLs one may consider either dead layers with a thickness of about the eciton radius and optical properties given by the background permittivity tensor or artificial layers of arbitrary thickness with no absorption in the spectral range of interest and optical properties generally different from those of the background. The thicknesses of the EFLs on different sides of the plate are considered to be the same. We solve the problems for the principal line A n = of the ecitonic spectrum of a heagonal crystal; the line is polarized perpendicularly to the C 6 ais. Note however that the solutions for the configurations in which the polarization of the incident light corresponds to the allowed polarization of the ecitonic transition (E C 6 ) can be used with slight corrections for nonpolarized ecitonic states in particular for ecitons in cubic crystals. Thus our results are a generalization of solutions of the corresponding problems for homogeneous singlecrystal plates obtained earlier for the case of normal incidence [6] as well as for the p component corresponding to the polarization of the allowed ecitonic state [7] and for the geometry of a mied eciton [8] at oblique incidence. Figure shows a schematic of the reflection and transmission in the above three-layer structure at normal incidence. The multiple reflections of light inside the optically homogeneous layers are taken into account as in [6] by introducing for each type of wave propagating in a certain layer a counterpropagating wave with the opposite direction of the wave vector k for normal incidence. For oblique incidence the intro- E 3 E refl E E incid E E ± ' E 4 E transm a' l a E ± C 6 d Fig.. Schematic of the reflection and transmission of light by a plane-parallel crystal plate with eciton-free layers on its surfaces. b l b' z X/05/ $ Pleiades Publishing Inc.

2 384 MOSKOVSKIŒ E refl E incid E incid E refl E ± ( ) z ë 6 ë 6 (c) E incid E incid E refl ë 6 ë 6 duced wave differs by the sign of the component k z. The pairs of the waves with k z > 0 and k z < 0 can be considered as superpositions of all the waves multiply reflected inside the corresponding layer if their amplitudes satisfy the complete set of boundary conditions at all interfaces. Let us denote the amplitudes of the waves propagating along the z ais in the layer adjacent to the front face by E and in that adjacent to the back face by E 3 and similarly the amplitudes of the waves propagating in the opposite direction by E and E 4 respectively. The phases of the waves E and E as well as of the incident and reflected waves will be measured from the outer face of the front EFL (z = 0); the phases of E 3 and E 4 as well as of the transmitted wave will be measured from the surface z = l + d; and the phases of the polaritonic waves from the inner boundary of the front layer with z = l ( l is the thickness of the EFL and d is the thickness of the inner layer in which the ecitonic states are ecited). In order for the system of boundary conditions to satisfy the symmetry requirements at oblique incidence one should specify them at the points a' a b and b' lying at the intersection of the z ais with the interfaces as is done in [7 8] for homogeneous plates. The origin of the phases is chosen in this case as in the case of normal incidence. E refl E ± E ± E ± z (b) (d) Fig.. Polarization of electromagnetic waves and orientation of the crystal ais for the s geometry (a) the p geometry (b) and the geometry of a mied eciton with C 6 (c) or C 6 z (d). z z We will consider four geometries of the oblique incidence of light on a plate of a heagonal crystal. In the first case the incident light is polarized perpendicularly to the plane of incidence (the s component of polarization) and the heagonal ais lies in the plane of incidence and is parallel to the surfaces of the crystal (C 6 ; Fig. a). The ecitonic transition A n = in this case will be allowed regardless of the angle of incidence of the light. This mutual orientation of the crystal ais the vector E the surfaces of the plate and the plane of incidence will be called the s geometry. In all other cases the incident light is polarized along the plane of incidence (the p component of polarization). In this arrangement the A n = transition will be totally allowed at any if the heagonal ais is normal to the plane of incidence (C 6 y; Fig. b). This configuration will be referred to as the p geometry. For the geometries shown in Figs. c and d with the p polarization of the incident light the C 6 ais lies in the plane of incidence. In one case this ais is parallel to the surfaces of the plate (C 6 ; Fig. c) and in the other case perpendicular to the surfaces (C 6 z; Fig. d). In this geometry the polaritonic waves in a heagonal crystal are mied (longitudinaltransverse) and for this reason such a geometry is called the geometry of a mied eciton (the mied eciton mode). For C 6 (Fig. c) in the limit of the normal incidence the A n = ecitonic transition is totally forbidden but the presence of the normal component of E at oblique incidence gives rise to lighteciton coupling which increases with the angle of incidence. When C 6 z (Fig. d) on the contrary the A n = transition at = 0 is totally allowed and at oblique incidence the effective oscillator strength of the ecitonic transition decreases with the angle of incidence. For eperimental studies the first version of the geometry of a mied eciton is more convenient because a decrease in the lighteciton coupling with decreasing angle of incidence makes it possibly to measure the transmittance in the resonance region for thicker plates [8]. As can be easily seen the geometry of normal incidence (Fig. ) is obtained from the s and p geometries at 0. The same limit for the configuration of the mied eciton mode corresponding to the schematic shown in Fig. d leads to the geometry of normal incidence for C 6 z. In the presence of the additional polaritonic waves the Mawell system of boundary conditions becomes incomplete. For this reason additional boundary conditions (ABCs) should be set at the inner interfaces of the EFLs. In this paper we use Pekar s ABCs which require the ecitonic contribution to the polarization to vanish at the crystal boundaries [ 3]: P ec z = 0 = 0. () OPTICS AND SPECTROSCOPY Vol. 98 No

3 TRANSMISSION AND REFLECTION OF LIGHT BY THIN SEMICONDUCTOR PLATES 385 THE s GEOMETRY We will consider the problem of seeking the comple amplitude transmittance and reflectance of a plane-parallel plate with surface EFLs using as an eample the s geometry. The dispersion of polaritons for a particular geometry can be obtained from the general tensor dispersion equation [] and from the dependence of the components of the permittivity tensor on the frequency ω and (taking into account the spatial dispersion) on the wave vector k. For the s geometry the dispersion equation has two solutions corresponding to the transverse normal polaritonic waves and E (comple amplitudes of the electric field strength) with the refractive indices n ± (ω ) which in the approimation of an isolated resonance have the form n ± ( ω ) = ε 0 + ηω ( ) ± η ( ω ) + α () ω ω ηω ( ) T β ε 0 ( β β ) sin + iγ = β (3) ω β T ω β T ε m *c α 0 ω = = = LT m *c β Here ε 0 is the background permittivity for the polarization E C 6 ω LT = ω L ω T is the longitudinaltransverse splitting ω L and ω T are the limiting frequencies of the transverse and longitudinal mechanical ecitons at k 0 γ is the decay constant m * is the effective mass of the eciton with the wave vector k C 6 m * is the effective mass of the eciton with the wave vector k C 6 and c is the speed of light. Due to the anisotropy of the effective mass n ± depends not only on the frequency but also on the angle of incidence. In all the geometries the solutions of the problems for plates with EFLs are based on the known solutions for homogeneous plates. In the s geometry at l 0 the continuity conditions for the tangential components of the electric and magnetic field strengths and the ABCs () at points a and b (Fig. ) have the form + ρ = + ' + E + E ' (4) ( ρ) cos = + ( ' ) + ( E E ') E + E ' = qe ( + + ' ) τ e iδ + E e iδ = τcos + e iδ + = ( ) + E e iδ E 'e iδ ( ) E 'e iδ (5) (6) (7) (8) E e iδ E 'e iδ + q e iδ + = ( + ) (9) ε q 0 = ± = n ± sin ε 0 n and δ ± is the phase incursion of the polaritonic waves between points a and b: δ ± = δ b ( E ± ) δ a ( E ± ) = ω ± d/c. The system of equations (4)(9) differs insignificantly from the system of boundary conditions for a homogeneous plate at normal incidence of light [6] (see also [3]). After the amplitudes of the polaritonic waves are eliminated the system acquires the form ρ = i[ ( + ρ)f τg] (0) τ = i[ ( + ρ)g τf] the functions F and G are given by F n + = ( ( + q) cos + cotδ + + q cotδ ) G q = ( + q) cos sinδ + sinδ System (0) and its solution τ ρ ig = G + ( + if) + F G = G + ( + if) () () in the geometry under consideration as well as in the p geometry and in the mied eciton mode with C 6 z can be reduced to a form coincident with the analogous results for the case of normal incidence [3 6] by deriving the corresponding epressions for F and G for each of the geometries. At l 0 the boundary conditions at the outer surfaces of the EFLs (at points a' and b') have the form + ρ = E + E (3) ( ρ) cos = 0 ( E E ) τ = E 3 + E 4 τcos = 0 ( E 3 E 4 ) (4) (5) (6) 0 = sin and n 0 is the refractive inde of the EFL. If a dead layer is considered as the EFL n 0 The phase shifts δ ± are actually comple quantities; i.e. they describe not only the changes in the phase but also the absorption in the medium. The epression given above is the same for all the geometries. In the p geometry the phase incursion δ can be found in a similar way. At normal incidence ± n ±. OPTICS AND SPECTROSCOPY Vol. 98 No

4 386 MOSKOVSKIŒ then n 0 = n 0 = is the background refractive inde for the polarization E C 6. The Mawellian boundary conditions at the inner surfaces of the EFLs (at points a and b) are (7) (8) (9) (0) is the phase difference between the points a' and a (b' and b) in the EFL. ABCs (6) and (9) include only the parameters of the polaritonic waves and the background permittivity. Therefore for the inner surfaces of the EFLs they remain valid. The system of equations (7)(0) (6) (9) differs from the system (4)(9) for a homogeneous plate by the substitutions + ρ Similarly on passing from Eq. (7) to Eq. (9) the following substitutions should be made: τ By making these substitutions in Eq. (0) and keeping in mind that the left-hand parts of these equations correspond to the left-hand parts of (5) and (8) (to within the factor cos) while the right-hand parts are obtained by eliminating the amplitudes of the polaritonic waves from Eqs. (5) and (8) using Eqs. (4) and (7) and the ABCs we obtain two equations that in combination with Eqs. (3)(6) comprise a system of si equations for the unknown amplitudes E E E 3 and E 4 and the sought τ and ρ. A solution of this system is given by the epressions for the comple amplitude transmittance and reflecε 0 E e iδ 0 E e iδ 0 + = + ' + E + E ' 0 E e iδ 0 E e iδ 0 ( ) = + ( ' ) + ( E E ') E 3 e iδ 0 and on passing from Eq. (8) to Eq. (0) + E 4 e iδ 0 = e iδ + E e iδ E 3 e iδ 0 E 4 e iδ 0 ( ) E 'e iδ = + e iδ + ( ) E e iδ E 'e iδ + ( ) δ 0 = δ a ( E ) δ a' ( E ) = ω 0 l/c E e iδ 0 + E e iδ 0 ( ρ) cos 0 E e iδ 0 E e iδ 0 ( ). E 3 e iδ 0 + E 4 e iδ 0 τcos 0 E 3 e iδ 0 E 4 e iδ 0 ( ). tance taking into account the spatial dispersion and surface EFLs in the s geometry τ ig = σ 0 G + ( σ + iσ 0 F) () σ ρ θ + σ 0 θ 0 ( F G ) + i( σ 0 θ σ θ 0 )F = () σ 0 G + ( σ + iσ 0 F) The quantities σ 0 σ θ 0 and θ entering these epressions are functions of the optical properties of the EFLs. They have the form σ 0 cosδ 0 i + ρ 0 = sinδ ρ 0 0 ρ σ = cosδ 0 i sinδ + ρ 0 0 θ 0 cosδ 0 i + ρ 0 = sinδ ρ 0 0 ρ θ = cosδ 0 + i sinδ + ρ 0 0 (3) ρ 0 is the amplitude reflectance from a semi-infinite medium with the optical properties of an EFL in the s geometry: ρ 0 cos = cos + 0 At l 0 formulas () and () are transformed into (). These results can be generalized to another variant of the s geometry with the heagonal ais directed along the z ais. For this purpose the longitudinal and transverse effective masses in () and (3) should be interchanged (β β ). The results are also valid for nonpolarized ecitonic states e.g. for polaritons in cubic crystals. In this case the components of the permittivity and effective mass tensors should be replaced by the corresponding scalar quantities which in particular makes the quantity n ± independent of the angle of incidence (see Eqs. () and (3)). THE p GEOMETRY For the p geometry (Fig. b) the tensor dispersion equation [] with the spatial dispersion taken into account is split into two equations ε ( ω k) = c k /ω ε ( ω k) = 0. The solutions of the first of them are two transverse polaritonic waves and E with the refractive indices n ± ( ω) = ε 0 + ηω ( ) ± η ( ω) + α (4) OPTICS AND SPECTROSCOPY Vol. 98 No

5 TRANSMISSION AND REFLECTION OF LIGHT BY THIN SEMICONDUCTOR PLATES 387 The solution of the second equation is the longitudinal wave E with the refractive inde n (5) Since the light in this case is polarized along the plane of incidence and the crystal is isotropic in this plane η(ω) in Eq. (4) is the limit of η(ω ) (3) at 0 and all the results presented below for the p geometry are also valid for the case of nonpolarized ecitonic transitions. The presence of the longitudinal wave makes the problem of transmittance and reflectance of the plate in this geometry much more cumbersome than for all other geometries considered here. The epressions for τ and ρ for a homogeneous plate in the p geometry were obtained in [7]. They have the form of Eq. () with the functions F and G defined by the formulas ηω ( ) ω ω T β ε 0 + iγ = β ω ω n L + iγ = = β F = ε 0 cos n + n ε 0 + cotδ + + q cotδ + q sin cotδ q sin 4 + (6) (7) For a plate with EFLs as in the case of the s geometry the problem is solved by setting up a correspondence between the system of boundary conditions at the inner surfaces of the EFLs and the system of boundary conditions for a homogeneous plate. The result q G = ε 0 cos +/ sinδ + + q / sinδ + q sin / sinδ q sin 4 + ( n q n ) ( σ + sin + sin 4 ) = ( n n + ) ( + σ sin + sin 4 ) ( n q n )( σ) = ( n + n ) ( + σ sin + sin 4 ) σ cosδ cosδ + + sinδ sinδ σ cos δ cos = = δ + sinδ sinδ σ q cosδ + cosδ = sinδ + sinδ = n sin δ = ω d c obtained has the form of Eqs. ()(3) with ρ 0 given by the epression Here ρ 0 has the meaning of the amplitude reflectance of a semi-infinite crystal with the optical parameters of the EFLs in the p geometry. THE MIXED EXCITON FOR C 6 z Consider the geometry of the mied eciton with C 6 z (Fig. d). The dispersion relation in this case has a form different from ε(ω k) = n (transverse waves) and from ε(ω k) = 0 (longitudinal waves). It has two solutions corresponding to the longitudinaltransverse waves with the refractive indices (8) and ε 0 is the permittivity for the polarization E C 6. As 0 Eq. (8) is transformed to the form of (4) with β substituted by β ( m * by m * ). This corresponds to passing to the geometry of normal incidence for which unlike Fig. C 6 z. As was already mentioned we have managed to reduce the solution of the problem for a homogeneous plate to the form of () with F and G in this case given by F n ± ηω ( ) ρ 0 n 0 cos 0 = n 0 cos ( ω ) = ε Z ( ) + sin + ηω ( ) ± η ( ω ) + α Z ω ω T β ε Z ( ) β sin + iγ = β ε Z ( ) ε sin ε Z ( )ω = αz = LT ε 0 ε 0 cos = ε ( Z ( ) ( + q Z ) cot δ + q + + Z cotδ ) G (9) In the presence of EFLs the problem is solved similarly to the cases considered above. The waves E E E 3 and E 4 in the dead layer with the background components of the permittivity tensor for the geometry of the mied eciton mode (for both C 6 z and C 6 ) will be longitudinaltransverse waves. In the case under β ε 0 cos = q ε Z ( ) ( + q Z ) sinδ Z sinδ q + ε Z ( ) Z = ε Z ( ) OPTICS AND SPECTROSCOPY Vol. 98 No

6 388 MOSKOVSKIŒ consideration (C 6 z) the result for the three-layer problem appears to be the same in its form as for the s and p geometries (see Eqs. ()(3)). In this case for EFLs with the optical properties of the dead layer the parameter 0 and the reflectance in the limit of l are equal to 0 = ε Z ρ 0 = 0 ε 0 cos ε 0 cos For EFLs with different optical properties one should use in Eq. (3) the corresponding epression for ρ 0. THE NORMAL INCIDENCE OF LIGHT At 0 the refractive indices n ± (3) acquire the form (4) the functions q(ω) and δ ± (ω) retain their form ± n ± 0 n 0 and the longitudinal wave is not ecited. The functions F and G given by () for the s geometry and by (6) (7) for the p geometry have the same limits equal respectively to (30) When the functions F and G in this form are used in () the results for a homogeneous plate coincide with those obtained by Pekar [3 6]. For a plate with EFLs epressions ()(3) with ρ 0 remain valid for the normal incidence: For the case C 6 z the passage to the limit 0 for the s geometry and the geometry of the mied eciton gives the same results to within the substitution in Eq. (4) of the transverse effective mass by the longitudinal mass. THE MIXED EXCITON FOR C 6 In the geometry of the mied eciton mode at C 6 (Fig. c) the dispersion equation taking into account the form of ε (ω k) has two solutions which determine the refractive indices of the two longitudinaltransverse polaritonic waves F = ( + q n cot δ + qn + + cotδ ) G n ± n q n = q sinδ + sinδ n ρ 0 0 = n 0 ( ω ) = ε X ( ) + sin + ηω ( ) ± η ( ω ) + α X ( ) ε 0 (3) ε X ( ) ε sin ε αx ( ) 0 ω LT sin = = β ε 0 ω ω ηω ( ) L β ε X ( ) β sin + iγ = β The amplitude transmittance and reflectance of a homogeneous plate of a heagonal crystal for this case were obtained in [8]. In the same paper they were used to find in this geometry the interference zeros in the transmission of thin CdSe crystals in the upper halfplane of the comple frequency. As a result it was shown that the calculations of the integral absorptance and additional terms in the KramersKronig dispersion relations performed with the use of the formulas obtained agree well with eperimental data in the vicinity of ecitonic transitions at low temperatures when the effects of spatial dispersion are important. The epressions for τ and ρ in the geometry under consideration can be reduced to a form that differs from () by the substitution of ρ for ρ: ig τ = G + ( + if) (3) + F G ρ = G + ( + if) F = ε ( 0 ( + q X ) cos cot δ + q + + X cotδ ) G = q (33) ε 0 ( + q X ) cos sinδ X sinδ q + ε X ( ) X = ε X ( ) The problem with the EFLs is solved in this geometry similarly to the previous cases. The solution also differs from the results obtained for all the geometries considered above by the substitution of ρ 0 for ρ 0 which according to Eq. (3) is equivalent to the interchanges σ 0 σ and θ 0 θ. Taking this into account the epressions for τ and ρ of the plate with the EFLs can be conveniently written in the form τ ig = σ G + ( σ 0 + iσ F) (34) σ ρ 0 θ 0 + σ θ ( F G ) + i( σ θ 0 σ 0 θ )F = (35) σ G + ( σ 0 + iσ F) Here the parameters σ 0 σ θ 0 and θ retain their previous meaning and when calculating them by formulas (3) one should use in the capacity of the quantity ρ 0 as before the amplitude reflectance of a semi-infinite crystal with the properties of the EFLs. In particular for the dead layer the quantities 0 and ρ 0 are equal to 0 ε X ρ 0 ε 0 cos = 0 = ε 0 cos OPTICS AND SPECTROSCOPY Vol. 98 No

7 TRANSMISSION AND REFLECTION OF LIGHT BY THIN SEMICONDUCTOR PLATES 389 R(ω) ln (D 0 /D(ω)) (ω ω T ) mev (ω ω T ) mev Fig. 3. The calculated reflectance spectra of a CdSe crystal in the region of the ecitonic state A n = for the p geometry: d = 0.3 µm; l = µm; γ/γ cr = 0.; = () 0 () 5 (3) 50 and (4) 70. The ais R(ω) refers to the lower spectrum; each subsequent spectrum is shifted upward by 0.5. Fig. 4. Calculated characteristics in the region of the principal line of the GaAs ecitonic spectrum for the p geometry: d = 0.3 µm; = 50 ; γ/γ cr = 0.; l = () 0 () (3) 0 and (4) 5 0 µm. The vertical ais refers to the lower spectrum; each subsequent spectrum is shifted upward by units. A detailed derivation of the formulas presented in this paper is given in []. EXAMPLES OF CALCULATED SPECTRA As an eample of the calculations by formulas () and () we present here the calculated spectra of reflectance and transmittance in the p geometry for the parameters of the principal ecitonic transitions of CdSe and GaAs crystals. Figure 3 shows the dependence of the reflectance spectra R(ω) = ρ(ω)ρ*(ω) in the region of the ecitonic state A n = of a CdSe crystal on the angle of incidence. The calculations were performed for a plate with a thickness d = 0.3 µm with surface dead layers having a thickness l = 60 Å for a value of the decay constant γ = 0.γ cr (γ cr = ε 0 ω LT β ). In the resonance region these spectra differ noticeably from those calculated with no EFL taken into account [7]. As the angle of incidence increases within the range of 0 50 the values of the interference reflectance peaks decrease while their positions remain practically the same. In the range of angles close to the Brewster angle for the background refractive inde the spectra change signif- icantly in terms of both the ratio of the peak amplitudes and their spectral positions. Figure 4 shows the dependence on the EFL thickness of the calculated functions ln(d 0 /D(ω)) D(ω) = τ(ω)τ*(ω) is the power-related transmittance and D 0 is its limiting value far from the resonance. It is convenient to consider the function ln(d 0 /D(ω)) as an absorptive characteristic of the crystal possessing integral properties of the absorptance [3]. The calculations were performed for the parameters of the ecitonic state with n = of a GaAs crystal at = 50 and γ = 0.γ cr. The thickness of the plate without the EFLs was taken as 0.3 µm and the EFL parameters were taken to be close to those of background. The calculations show that with increasing l the main absorption peak increases while the interference peaks in the shortwavelength region are suppressed. In this case the peaks related to the usual (predominant in amplitude) wave are suppressed to a greater etent and for this reason the double periodic structure of the spectrum becomes more pronounced. The analysis of the calculated reflectance and transmittance spectra shows that the presence of a large number of parameters that can be varied in the calcula- OPTICS AND SPECTROSCOPY Vol. 98 No

8 390 MOSKOVSKIŒ tions etends the possibilities of identification of one or another effect associated with specific features of the polariton dispersion with the multibeam interference in the plate or with surface inhomogeneities. ACKNOWLEDGMENTS The author is grateful to L.E. Solov ev for his interest in this study and useful discussions. REFERENCES. S. I. Pekar Zh. Éksp. Teor. Fiz (957) [Sov. Phys. JETP (957)].. V. M. Agranovich and V. L. Ginzburg Crystal Optics with Spatial Dispersion and Ecitons nd ed. (Nauka Moscow 979; Springer New York 984). 3. S. I. Pekar Crystal Optics and Additional Light Waves (Naukova Dumka Kiev 98) [in Russian]. 4. V. A. Kiselev B. V. Novikov and A. E. Cherednichenko Eciton Spectroscopy of Near-Surface Region of Semiconductors (St.-Peterb. Gos. Univ. St. Petersburg 003) [in Russian]. 5. J. J. Hopfield and D. G. Thomas Phys. Rev (963). 6. S. I. Pekar Zh. Éksp. Teor. Fiz (958) [Sov. Phys. JETP 7 83 (958)]. 7. Yu. V. Moskalev S. B. Moskovskiœ and L. E. Solov ev Opt. Spektrosk (003) [Opt. Spectrosc (003)]. 8. S. B. Moskovskiœ A. B. Novikov and L. E. Solov ev Zh. Éksp. Teor. Fiz (994) [JETP (994)]. 9. S. B. Moskovskiœ A. B. Novikov and L. E. Solov ev Fiz. Tverd. Tela (Leningrad) (988) [Sov. Phys. Solid State (988)]. 0. S. R. Grigor ev S. B. Moskovskiœ A. B. Novikov and L. E. Solov ev Vestn. Leningr. Univ. Ser. 4: Fiz. Khim. No (987).. S. B. Moskovskiœ A. B. Novikov O. S. Omegov and L. E. Solov ev Fiz. Tverd. Tela (Leningrad) (99) [Sov. Phys. Solid State (99)].. S. B. Moskovskiœ Interference Reflection and Transmission of Light by Thin Crystalline Plates in the Eciton Spectral Region Taking into Account Spatial Dispersion and Noneciton Layers at Surfaces (Yarosl. Gos. Pedagog. Univ. Yaroslavl 004) [in Russian]. 3. S. B. Arkadova Yu. V. Moskalev S. B. Moskovskiœ and L. E. Solov ev Opt. Spektrosk (004) [Opt. Spectrosc (004)]. Translated by V. Zapasskiœ OPTICS AND SPECTROSCOPY Vol. 98 No