~Pergamon
`
`Solid State Communications, Vol. 96, No. 10, pp. 793-798, 1995
`Copyright© 1995 Elsevier Science Ltd
`Printed in Great Britain. All rights reserved
`0038-1098/95 $9.50 + .00
`
`0038-1098(95)00460-2
`
`OPTICAL STUDIES OF ZnSe-ZnS/GaAs(l 0 0) SINGLE QUANTUM WELLS GROWN BY
`PHOTO-ASSISTED VAPOR PHASE EPITAXY
`
`V.V. Tishchenko,* Y.S. Raptis and E. Anastassakis
`
`National Technical University, Department of Physics, Athens 157 80, Greece
`and
`N.V. Bandar
`
`Institute of Physics, Ukranian National Academy of Sciences, 252650 Kiev, Ukraine
`
`(Received 3 July 1995 by J. Kuhl)
`
`Confinement effects of phonon and excitonic modes in two mono(cid:173)
`layers-thickness ZnSe-ZnS single quantum wells (SQWs) grown
`through photo-assisted vapor phase epitaxy (PA VPE) have been
`investigated by means of Raman, photoluminescence (PL) and reflec(cid:173)
`tion spectroscopy. It has been found that the frequency of the SQW
`longitudinal optical (LO) phonon mode is red shifted by 2.1 cm- 1
`relative to the LO phonon frequency of bulk ZnSe. This shift has been
`attributed to the combined opposite action of strain and confinement
`effects. The PL data have shown that the ls state of then = 1 subband
`heavy-hole (hh) excitonic band is blue shifted by 188 meV relative to the
`energy of free excitons in ihe buik materiai. Largeiy responsibie for this
`shift is the quantum confinement of electrons and holes. In addition,
`the transitions involving the 2s state of the hh excitons have been clearly
`observed. The 2s- ls energy splitting was found to be 38meV. From
`this result, the binding energy of the ls hh exciton has been estimated to
`be 44meV.
`
`Keywords: A. quantum wells, B. epitaxy, C. optical properties.
`
`1. INTRODUCTION
`
`IN RECENT YEARS, II- VI quantum well systems
`based on wide-gap semiconductors have been heavily
`studied because of their extensive application in solid(cid:173)
`state blue light emitters [1 ]. Most of these studies have
`been carried out on structures grown through either
`molecular beam epitaxy or metal-organic chemical
`vapor deposition. Both techniques are known to
`produce high quality quantum wells (QWs) for such
`applications.
`This paper presents the results of Raman, PL and
`reflection spectroscopic investigations, of ZnSe- ZnS
`SQWs produced by a simpler, more versatile and far
`more inexpensive technique, namely PA VPE [2]. The
`
`• Permanent address: Institute of Physics, Ukranian
`National Academy of Sciences, 46 Prospect Nauki,
`252650 Kiev, Ukraine.
`
`results provide clear evidence of the confinement of
`excitons and LO phonons in ZnSe (11 A)-ZnS (60 A)
`SQWs, thus revealing the presence of sharp interfaces.
`In addition, the excitonic binding energy in such
`SQWs was found from the difference in the energies
`of the ls and 2s states associated with the heavy-hole
`(hh) n = 1 excitonic subband. This finding is based on
`a recent theoretical model which treats excitons in
`QWs as quasi-particles in an isotropic space of
`fractional dimensionality; the exact value of dimen(cid:173)
`sionality depends on the degree of anisotropy of the
`Coulomb attraction between electrons and holes [3].
`
`2. EXPERIMENT AL DETAILS
`
`The ZnSe- ZnS SQWs were grown on a GaAs(l 0 0)
`substrate from the gas phase in a quartz reactor of the
`horizontal type, designed to have a high temperature
`gradient (250°C cm- 1
`) in the deposition zone. During
`Nanoco Technologies, Ltd
`EXHIBIT 1008
`
`793
`1 of 6
`
`

`
`794
`
`OPTICAL STUDIES OF ZnSe-ZnS/GaAs(l 00) SINGLE QUANTUM WELLS Vol. 96, No. 10
`
`293.0
`
`268.9
`
`10
`
`:;)
`
`5
`
`a
`
`TOqw
`
`LO w
`
`- ~ ,...
`"'
`....
`[/)
`z
`..:
`f-
`~
`
`the epitaxy, this zone was illuminated by the 441.6 nm
`line of an He-Cd laser. This method of growth, details
`of which can be found in [2] provides the conditions
`required for obtaining device quality epilayers with
`accurately controlable thicknesses, and sharp inter(cid:173)
`faces. To observe the expected confinement, 11 A-thin
`ZnSe layers were grown and sandwiched between 60 A(cid:173)
`thick ZnS barriers. The thicknesses stated here, were
`predetermined by the well-known growth rate and the
`duration of growth; the latter parameter was accurately
`controlled by a computer. The interface roughness in
`these samples was limited to only one atomic mono(cid:173)
`layer (about 2.83 A), as evidenced by the narrow exci(cid:173)
`tonic width in the PL spectra.
`The Raman measurements were carried out at
`room temperature in the z(x, x + y)z scattering geo(cid:173)
`metry (z being along the growth direction). A triple
`monochromator (Jobin Yvon T64000, micro-Raman)
`with a CCD detector was used. The power of 514. 5 nm
`line of an Ar laser, applied on the surface of the
`sample did not exceed 0.5 mW, to avoid shifting of
`the Raman bands caused by heating. The Raman
`spectra of a bulk ZnSe crystal were measured in
`parallel with those from the SQWs and used as a
`reference in determining the actual shift of the Raman
`bands from the structures under study.
`The experimental set-up for the PL measurements
`included a I 0 mW cw He- Cd laser as an excitation
`source (325.0 nm), weakly focused to avoid laser heat(cid:173)
`ing, a PC-controlled double monochromator with a
`photomultiplier tube, and a variable-temperature opti(cid:173)
`cal cryostat operating at either a helium-immersion or
`gas-flow mode. The temperature stability was within
`O. l K h- 1
`• The spectroscopic and detection set-up of
`the PL experiments was also employed for the reflection
`experiments, using a tungsten halogen lamp.
`
`3. EXPERIMENTAL RESULTS AND
`DISCUSSION
`
`Figure l(a) shows a typical Raman spectrum
`taken from the ZnSe-ZnS SQWs described above.
`The spectrum exhibits a strong LO phonon band at
`293.0cm- 1 and a relatively weak TO band at 268.9 cm- 1
`both originating from the GaAs substrate. In the
`spectral region of ZnSe, two weak bands denoted
`
`
`by LOqw (250.9cm- 1) and TOqw (206.3cm- 1) are
`observed. The frequencies of these bands were deter(cid:173)
`mined with an accuracy of0.4cm- 1 through fitting of
`Lorentzian curves to the experimental line shapes. For
`this fitting, the bandwidths, peak frequencies and
`peak heights of the observed bands were used as
`adjustable parameters. The resulting spectrum is
`shown in Fig. l(b). It should be noted that no
`
`c
`
`0
`
`200
`
`250
`
`300
`-1
`RAMAN SHIFT {cm )
`
`350
`
`Fig. I. Raman spectra of (a) ZnSe (ll A)-ZnS (60A)
`SQW, and (c) ZnSe epilayer; (b) fitting Lorentzian
`curves to spectrum (a). The arrow indicates the value
`of the LO phonon frequency for bulk ZnSe. The
`spectra are displaced for clarity.
`
`Raman scattering was observed from the ZnS barriers
`because of the low scattering cross section of ZnS
`compared to ZnSe.
`The most interesting feature of Fig. l(a) is the shift
`of the LOqw mode by 2.1 cm- 1 to lower frequencies
`relative to the observed bulk value (253 cm- 1 ). This
`shift is caused by the combination of compressive
`strain and confinement effects in the ZnSe well. We
`write the frequency of the LOqw band as
`Wqw = Wo + 8wst + DWconfi
`( l)
`where w0 is the bulk frequency of the LO phonon, and
`Ow51 and bwconf are the strain- and confinement(cid:173)
`induced shifts, respectively.
`In order to separate the effect of confinement, we
`measured the Raman spectrum from a 60 A ZnSe
`epilayer grown on a GaAs(l 00) substrate [Fig. l(c)].
`The spectrum displays a blue shift for the ZnSe LO
`mode, denoted by LOepJ. equal to ,...., 1 cm - t, relative to
`the bulk value. Given that the influence of confine(cid:173)
`ment on the LO phonon of the ZnSe epilayer with a
`thickness equal to or larger than 60 A is negligible [4],
`one can conclude that the shift in our 60 A epilayer is
`largely caused by the lattice mismatch strains. In the
`accordance with the notation of [5], this shift can be
`expressed as
`- L C12 - L) II
`8w51 = Wo K1 2 - ~K11 f
`(
`,
`- L
`- L
`where K11 and K12 are the LO phonon deformation
`potentials of ZnSe normalized to w5, C 11 and C 12 are
`11 = (a" / a0 ) -
`l is
`elastic stiffness components, and 1:
`the in-plane isotropic strain component (a" being the
`lattice constant of the ZnSe epilayer parallel to the
`interface, and a0 the bulk lattice constant).
`
`(2)
`
`2 of 6
`
`

`
`Vol. 96, No. 10 OPTICAL STUDIES OF ZnSe-ZnS/GaAs(l 00) SINGLE QUANTUM WELLS
`It is noted that the 60 A ZnSe epilayer is pseudo(cid:173)
`morphic, as its thickness is far below the critical value
`(1500A) for the onset of misfit dislocations [6].
`Furthermore, the critical thickness for ZnS grown
`on a GaAs(l 0 0) substrate is about 100 A [7]. Thus,
`in all layers of our SQWs the in-plane lattice constants
`a" are equal to the lattice constant of the substrate.
`11 for ZnSe is
`This means that the in-plane strain f.
`equal to the lattice misfit between ZnSe and GaAs.
`Setting /' = -0.27% [6], we find from equation (2)
`that 6ws1 is equal to 0.96 cm- 1
`• This upward shift
`is close to the experimental value obtained directly
`from the Raman spectra of the ZnSe epilayer.
`The physical constants of ZnSe used in all our
`calculations are listed in Table 1. Assuming that the
`strain-induced shift 6ws1 is the same in the SQW as
`in the epilayer, we finally find from equation (1)
`DWconf ~ - 3. l cm- 1
`•
`We now proceed to determine the type of confined
`LO modes involved. Their frequencies can be taken
`from the bulk phonon dispersion curve, and the
`magnitudes of their wavevectors calculated from [8]
`7r
`qm = (k + 6)a_l_ m ,
`
`6~:nf + J y = 1 + {I - ~ [ l - cos (a; qm)] f 1
`
`2
`
`,
`
`(6)
`
`The strength of confinement decreases as the mode
`spreads into the adjacent barriers. To estimate the
`magnitude of this effect in our SQWs in terms of the
`leakage parameter 8, we have calculated the red shifts
`of two LO phonon modes (m = 1, 2) in the confined
`state as a function of 6. By definition
`
`795
`
`(4)
`
`where w(qm) is defined from a phenomenological
`expression for the bulk LO phonon dispersion [4]
`
`w2(q) =A+ {A 2
`- B[l - cos(7rq)]} 1
`/ 2
`(5)
`with q in units of 2n / a0, A = 3 .2 x l 04 cm - 2 and
`• Noticing that w5 = w2(0) = 2A,
`B = 4.5 x 108 cm-4
`and ignoring any effects of strain on the bulk dis(cid:173)
`persion relation, we finally find from equations (4)
`and (5)
`
`2 (
`
`m = 1,2, . . . ,k.
`
`(3)
`
`Odd (even) values of the index m correspond to
`B2{A 1) phonon symmetry. a.J..
`is the ZnSe lattice
`constant normal to the interface and can be obtained
`from
`the definition of the corresponding strain
`f _j_ = (a_j_ /a0 ) - 1 and
`the well-known
`relation
`f _j_ = -{2C1 if C12 )f
`11 and f_j_,
`11 (Poisson's
`between f.
`law along [00 l]). The parameter 6 in equation (3)
`accounts for the leakage of the LO phonon from the
`confined state and takes different values for each
`individual mode; k stands for the number of ZnSe
`monolayers of the well, and is equal to 2 in the present
`case.
`
`where qm
`is taken from equation (3) and ~ =
`Bf A 2 = 0.44. The solutions of equation (6) for
`6wconf as a function of 6 are shown in Fig. 2 for
`m = l, 2. Our estimated (from the Raman data)
`value of 6wconf = -3.l cm- 1 yields m = l and
`6 = 0.38. The value of 6 is smaller than that usually
`encountered in the literature ( 6 = 1, [9]). It follows
`that the strongest mode confined in our 11 A SQW is
`of B2 symmetry, m being odd. Furthermore, the
`smaller the value of 8 the less phonon leakage
`occurs into the ZnS barrier. Given the fact that the
`amount of leakage depends critically on the sharpness
`of the interfaces, the present value of 8 reflects the high
`quality of the interfaces which have small total surface
`of one atomic monolayer high interfacial defects.
`
`Table I. Physical parameters of bulk ZnSe used in the present calculations
`
`Parameter
`
`Lattice constant
`LO phonon frequency
`LO phonon deforma tion
`potentials normalized to w5
`Elastic stiffnesses
`
`Electronic deformation potentials:
`hydrostatic
`shear
`Rydberg consta nt for bulk exciton
`
`a [11].
`
`b This work.
`
`c [5].
`
`d [7].
`
`e [13].
`
`Denotation (units)
`
`ao(A)
`w0 (cm- 1
`)
`- L
`K11
`- L
`K 12
`C 11 (GPa)
`C 12 (GPa)
`
`a(eV)
`b(eV)
`£ 0 (meV)
`
`3 of 6
`
`Value
`
`5.66763
`253b
`-0.94c
`-2.28c
`85.9c
`50.6c
`
`

`
`796
`
`OPTICAL STUDIES OF ZnSe-ZnS/GaAs(l 00) SINGLE QUANTUM WELLS Vol. 96, No. 10
`
`40
`
`30
`
`:i
`"'
`t 20
`Cf) z
`"' f-z
`
`10
`
`0
`
`ls
`
`a
`
`15
`0.5
`LEAKAGE PARAMETER Ii
`
`Fig. 2. Confinement-inquced shifts oJ the LO phonon
`frequency in ZnSe (I I A)-ZnS (60A) SQWs relative
`to the bulk frequency, as a function of the leakage
`parameter b, for the two possible values of m.
`
`Next we examine the behavior of the excitonic
`modes in the present SQWs. Figure 3(a) shows the
`intense excitonic PL band originating from then= l
`hh excitons and located at 414.4nm (2.991 eV). The
`most direct evidence for this assignment comes from
`the reflection spectrum shown in Fig. 3(b). The latter
`displays the typical excitonic feature at the same
`energy the dominant PL band appears. An additional
`weak feature at 388.6 nm (3.19 eV) is clearly visible in
`the reflection spectrum.
`In a
`recent
`theoretical work, Hayashi and
`Katayama used a modified Kroning- Penney model
`and taking into consideration the difference between
`the electron mass of ZnSe and that of ZnS they
`studied the excitons in ZnSe- ZnS strained SLs and
`SQWs [10]. From their results it follows that the
`energy levels of both systems are practically the
`same. In fact it was calculated in [1 OJ that the energy
`gap related to the hh excitons in ZnSe (11 A)-ZnS
`(50 A) SQW should be 2.99 eV. We therefore conclude
`that the low-energy feature displayed in Fig. 3(b) at
`414.4nm corresponds to the hh exciton.
`As already mentioned, the reflection spectrum also
`exhibits a high-energy structure located 199 meV
`higher than the hh excitonic feature; most likely this
`structure is related to the th excitons. The simple
`Kroning- Penney model which we employed for the
`finite 11 A SQW leads to an energy separation
`between the lh and hh states of more than I 00 me V.
`Our calculation is based on the bulk values for the th
`and hh masses (0.145m0 [13] and 0.6m0 [6], respec(cid:173)
`tively), provided that the offsets of the conduction and
`valence bands are 77meV and 815meV, respectively
`[12]. More sophisticated models which take into
`
`360
`
`380
`
`400
`
`420
`
`440
`
`WAVELENGTH (nm)
`
`Fig. 3. Photolumine~cence (a) ~nd reflection (b)
`spectra of ZnSe (11 A)-ZnS (60A) SQW at 4.5 K.
`The spectra are displaced for clarity.
`
`account the renormalization of the effective mass of
`both electrons and holes inside QWs would have
`probably resulted in an estimation of the lh- hh
`splitting for our SQWs closer to the observed value
`of 199meV.
`The blue shift of the 2.991 eV excitonic feature in
`an SQW with respect to the 2.8027 eV energy level of
`the free exciton in bulk ZnSe [ 13] is clearly seen in Figs
`3(a) and 3(b). This shift of 188 meV is attributed both
`to the strain effect caused by the ZnS- ZnSe lattice
`mismatch and to the quantum confinement of elec(cid:173)
`trons and holes. The shifts of the hh and lh valence
`bands with respect to the conduction band are written
`[ 11]
`bU = ( - 2a C11 - C12 ± b Cu + 2C12) E",
`C11
`C11
`where the + ( - ) sign corresponds to the hh (lh) bands,
`and a and b are the electronic deformation potentials
`for the hydrostatic and shear part of the shift, respec(cid:173)
`tively. We have estimated from equation (7) that the
`strain-induced shifts are 4.9 meV and 20.0 meV for the
`Ith and lh bands, respectively. These values are at most
`5% of the total shift observed. It is therefore suggested
`that the observed blue shift is largely caused by
`confinement.
`It is interesting to notice the presence of a
`relatively weak PL band at 409.2 nm (3.029 eV). As
`the temperature is increased over 4.5 K, this band
`becomes weaker compared to the dominant low(cid:173)
`energy PL band, and finally disappears around 16 K
`(Fig. 4). The same band cannot be observed at
`relatively low incident intensities, as shown in Fig. 5
`[14]. Based on these observations, we argue that the
`3.029 eV PL band originates from exciton transitions
`
`(7)
`
`4 of 6
`
`

`
`Vol. 96, No. 10 OPTICAL STUDIES OF ZnSe-ZnS/GaAs(l 00) SINGLE QUANTUM WELLS
`
`797
`
`where £ 0 is the effective Rydberg constant for the bulk
`exciton and a is the dynamic space fractional dimen(cid:173)
`sion which measures the anisotropy of the electron(cid:173)
`hole Coulomb interaction. The fractional dimension
`is related to the 2s-1s splitting in a simple way [3]
`
`E2s - Eis
`Eo
`
`16a
`= (0:2-1)2·
`
`(9)
`
`Using the experimental value for the 2s- ls splitting
`(38 meV), we estimate that a= 2.35. As a result, the
`binding energy of the Is hh exciton is 44 me V, using
`the value of £ 0 from Table 1. Despite the very narrow
`ZnSe well, the exciton seems not to behave as a purely
`2D quasi-particle. Such deviation from
`the 2D
`behavior is very likely to be caused by the very small
`conduction band offset (77 meV) which results in a
`partial delocalization of the electron. Thus, the
`spreading of the electron into the ZnS barrier partially
`restores a 3D character for the motion of the excitonic
`center of mass.
`
`4. CONCLUSIONS
`
`80 ~
`
`-
`
`'
`60 J_
`I
`!
`::
`"'
`t: -W _;_
`;;;
`I
`z
`~ z
`- 20 -j-
`
`1;\,
`
`c -----·
`
`b - - - --
`
`/ I\\- \
`' I
`I
`I
`:
`
`\
`
`'
`
`' ------------
`
`-------~
`
`2s
`
`0 r[__a t------+·----+ -\---t--+-1 ___,j
`
`405
`
`410
`
`415
`
`420
`
`425
`
`WAVELENGTH (nm)
`Fig. 4. P,hotoluminescence spectra of ZnSe (11 A)(cid:173)
`ZnS (60 A) SQW at various temperatures: (a) 4.5 K,
`(b) 10 Kand (c) 16 K. The spectra have been normal(cid:173)
`ized to the intensity of the ls band at 2.991 eV and are
`displaced for clarity.
`
`involving the first excited state of the n = I hh free
`exciton, i.e., the 2s state, which is populated mainly
`through scattering events. The latter argument is open
`to further study.
`The last and most important step is to estimate the
`exciton binding energy. This is accomplished by
`following the simple analytical method developed in
`[3]. According to those results the binding energy of
`the ls exciton is given by
`
`E _ _ 4Eo
`( 0: - 1 )2 ,
`b -
`
`i
`
`80 -~
`I
`-: 60 r
`"
`I
`~
`!
`c 40 _!_
`~
`i
`?E; 20 L
`!
`
`E--
`
`;
`
`Optical studies were carried out on PAVPE-grown
`ZnSe-ZnS SQWs with thickness of two ZnSe mono(cid:173)
`layers. The sharpness of interfaces of these samples
`was confirmed by the observation of confined LO
`phonon modes in the Raman spectra. The low(cid:173)
`temperature PL spectra of these SQWs were
`dominated by the intense emission of then = 1 ls hh
`excitons, and accompanied by a relatively weak
`emission involving the 2s state. From the experimen(cid:173)
`tal value for the 2s- ls splitting the exciton binding
`energy was estimated. It is concluded that the
`behavior of excitons in very thin ZnSe-ZnS SQWs
`is not described by a purely 2D model. Fractional(cid:173)
`dimensional space with dimension of 2.35 should be
`introduced to describe actual excitonic problems in
`these quantum wells. On the contrary, in ZnSe(cid:173)
`ZnS0_18Se0_82 SLs, where the QWs are of much larger
`width (237 A) and considerably smaller in depth
`[:S25 meV for electrons [6], compared to 77 meV of
`our SQWs], the fractional dimensionality is 2.995,
`suggesting nearly 3D character for the free excitons
`in those QW structures [15].
`'~
`0 i-
`to
`Acknowledgements - The authors are grateful
`L' ~~~~-+~~-+-~~-+-~~-t----- f
`420
`425
`405
`410
`-11 5
`Dr A. Kovalenko for supplying the samples. One
`of us (V.V.T.) is grateful to Dr P. Lilley for the
`fruitful discussions on the PL data during a visit
`to the University of Manchester made possible
`through a British Council grant. The same author
`acknowledges financial support from the National
`Technical University, Athens, during his stay in
`Greece.
`
`(S)
`
`~
`j
`J
`
`ls
`(1
`i
`\
`I
`"
`\
`!
`/ '\
`,'
`·~
`)
`'I
`I
`'\
`I
`I
`I
`\
`i
`
`'
`
`b __ __.---/'
`
`, ,_____________
`
`JI
`
`WAVELENGTH (nm)
`
`Fig. 5. ~hotoluminescence spectra of ZnSe (11 A)(cid:173)
`ZnS (60 A) SQW at 4.5 K for various power densities
`of the He- Cd laser excitation source: (a) 0.1310 , (b)
`0.36/0 and (c) /0 = 60Wcm- 2
`. The spectra are dis(cid:173)
`placed for clarity.
`
`5 of 6
`
`

`
`798
`
`OPTICAL STUDIES OF ZnSe-ZnS/GaAs(l 00) SINGLE QUANTUM WELLS Vol. 96, No. 10
`
`11.
`
`10. H. Hayashi & S. Katayama, Phys. Rev. B39,
`8743 (1989).
`J. Gutowski, N . Presser & G. Kudlek, Phys.
`Status Solidi ( a) 120, 11 (1990).
`12. Y. Yamada & Y. Masumoto, in 20th Int.
`Conf. Phys. Semicond. Thessaloniki, Greece,
`1990 (Edited by E.M. Anastassakis & J .D.
`Ioannopoulos), Vol. 2, p. 941. World Scientific,
`Singapore (1990).
`13. H. Nelkowski & H.J. Schulz, in Landolt(cid:173)
`Bornstein Numerical Data and Functional Rela(cid:173)
`tionships in Science and Technology (Edited by
`0. Madelung, H. Schulz & H. Weiss), Group
`Ill, Vol. 17, Subvol. b, p. 126. Springer, Berlin
`( 1982).
`14. The blue shift of the main excitonic band with
`increasing laser power refers to the tail of loca(cid:173)
`lized states due to the formation of islands and
`valleys at the ZnSe-ZnS interface; this point will
`be discussed in a future communication.
`15. R. Tommasi, M. Lepore, M.C. Netti, J.M.
`Catalano & I. Suemune, Phys. Rev. B49, 14367
`(1994).
`
`REFERENCES
`I. A.V. Nurmikko & R.L. Gunshor, Phys. Status
`Solidi (b) 173, 291 (1992).
`2. M.S. Brodin, N .V. Bondar, V.V. Tishchenko,
`A.V. Kovalenko & A.Yu. Mekekechko,
`Quantum Electron (USA ) 23, 532 (1993). Also,
`A.V. Kovalenko & V.V. Tishchenko, in Proc.
`Int. Conf Optical Properties of Nanostructures,
`Sendai, Japan (1994); Jpn J. Appl. Phys. 34,
`Suppl. 34-1, 209 (l 995).
`.
`3. H. Mathieu, P. Lefebvre & Ph. Chnstol, Phys.
`Rev. 846, 4092 (1992).
`4. D.J. Olego, K. Shahzad, D.A. Gammack &
`H . Cornelissen, Phys. Rev. B38, 5554 (1988).
`5. E. Anastassakis, Solid State Commun. 84, 47
`(1992).
`6. K. Shahzad, D.J. Olego & Ch.G. Van de Walle,
`Phys. Rev. B38, 1417 (1988).
`7. T. Taguchi, Y. Kawakami & Y. Yamada,
`Physica Bl91, 23 (1993).
`8. M. Cardona, in Light Scattering in Semiconduc(cid:173)
`tor Structures and Superlattices (Edited by D.J.
`Lockwood & J.F. Young), p. 19. Plenum Press,
`New York (1991).
`J.L. Brebner, R. Leonelli,
`9. C.A. Tran,
`M. Jouanne & R.A. Masut, Phys. Rev. B49,
`11268 (1994); Z.P. Wang, H.X. Han & G.H.
`Li Phvs. Rev. B42, 9693 (1990); G. Faso!,
`M'. Tanaka, H. Sakaki & Y. Horikoshi, Phys.
`Rev. B38, 6056 (1988).
`
`6 of 6