The self-organized quantum dot (QD) formation in InGaAs/GaAs superlattices grown by molecular beam epitaxy was investigated by the high-resolution X-ray diffraction technique. The investigated samples had the identical structure consisting of fifteen periods of {InxGa1−xAs (8 ML)/GaAs (26 ML)} with the nominal In concentration x = 0.2. The diffraction profiles and reciprocal lattice maps for these samples have been measured at symmetrical (004) reflection by using the triple-crystal X-ray diffractometer. The analysis of the measured data was performed by using the proposed diffraction model based on the statistical theory of dynamical X-ray scattering in imperfect single crystals and multilayer structures

Klad’ko, V.P.

Kyslovs’kyy, Ye.M.

Len, E.G.

Lizunova, S.V.

Molodkin, V.B.

Olikhovskii, S.I.

Sheludchenko, B.V.

Skakunova, O.S.

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 4 No 1, 01PCSI03(3pp) (2015)   2304-1862/2015/4(1)01PCSI03(3) 01PCSI03-1  2015 Sumy State University Dynamical X-Ray Diffraction Characterization of the Self-Organized  Quantum Dot Formation In Imperfect Semiconductor Superlattices  S.V. Lizunova1,*, O.S. Skakunova1, S.I. Olikhovskii1, E.G. Len1, V.B. Molodkin1, V.P. Klad’ko2,  Ye.M. Kyslovs’kyy1, B.V. Sheludchenko1  1 G.V. Kurdyumov Institute for Metal Physics of the NASU, 36, Vernadsky Blvd., 03680 Kyiv, Ukraine 2 V. Lashkaryov Institute of Semiconductor Physics of the NASU, 45, Pr. Nauki, 03680 Kyiv, Ukraine  (Received 31 May; published online 27 August 2015)  The self-organized quantum dot (QD) formation in InGaAs/GaAs superlattices grown by molecular beam epitaxy was investigated by the high-resolution X-ray diffraction technique. The investigated samples had the identical structure consisting of fifteen periods of {InxGa1−xAs (8 ML)/GaAs (26 ML)} with the nom-inal In concentration x = 0.2. The diffraction profiles and reciprocal lattice maps for these samples have been measured at symmetrical (004) reflection by using the triple-crystal X-ray diffractometer. The analy-sis of the measured data was performed by using the proposed diffraction model based on the statistical the-ory of dynamical X-ray scattering in imperfect single crystals and multilayer structures.   Keywords: quantum dots, superlattice, X-ray diffraction, diffuse-dynamical diffractometry.   PACS numbers: 61.05.cc, 61.05.cp, 61.72.Dd, 68.35.Dv, 68.65.Ac, 68.65.Hb                                                             * svetlana.lizunova@gmail.com 1. INTRODUCTION  Self-organized quantum dots (QDs) in superlattices grown by molecular beam epitaxy are of great interest due to their potential applications in modern optoelec-tronic devices, such as lasers, optical memories, infra-red photodetectors, etc. [1, 2]. However, because of insufficiently good understanding the complicated self-organization process of nanosize islands formation in thin films, particularly, in the InGaAs/GaAs superlat-tice system, the production of QD-based devices has the unreliable yield. The present work is devoted to the development of X-ray dynamical diffraction technique for reliable mon-itoring QD structures and, particularly, for its using in the investigation of InGaAs/GaAs superlattice systems.  2. THEORETICAL MODEL  2.1 Coherent scattering  According to results of the generalized dynamical theory of X-ray diffraction by imperfect single crystals [3–5], the coherent wave field in a crystal with homo-geneously distributed defects can be represented in the two-wave approximation as the sum of transmitted and diffracted waves for each  polarization state (and ):        T SD D D r r r ,      0T 0 eiD D K rr ,  S eiD D  HK rHr , (1)  where  = 1,2, r is the space coordinate, 0D  and DH  are the amplitudes of transmitted and diffracted coherent plane waves, respectively, H is the reciprocal lattice vector, 2K    is the module of the wave vector K of an incident plane wave, and  is the wavelength. To determine the amplitude reflectivity of the total multilayered system    1 2 0R b E E H ,  where b  0H is the parameter of diffraction asym-metry, 0 and H are direction cosines of wave vectors of incident (K) and scattered (K) plane waves, respectively; Е0 and ЕН are amplitudes of the incident and coherently scattered plane waves in a vacuum, respectively, it is necessary to find amplitudes 0MD  and MDH of a wave field in M th layer, which are connected as well to the amplitude of the wave reflected in (M  1) th layer, etc. The recurrence relation between amplitude reflec-tion coefficients of adjacent layers can be determined as follows:   2 211( )1j j j j jjj j jr R t rRr R , (2)     10 0CE CE        H H H H ,   where jr  and jt  are amplitude reflectivity and trans-missivity of j th layer, respectively, C is the polariza-tion factor equal to 1 or Bcos2  for  and  polariza-tion, respectively, G  are Fourier components of the perfect crystal polarizability (G  0, H).  2.2 Diffuse scattering  According to [3], the diffuse scattering (DS) ampli-tude from j th layer can be represented as    , jj j j j jf D F e   H G HGGK K , (3)   1Mi jj i id     H , 0 dsii i    , 1,2  .   S.V. LIZUNOVA, O.S. SKAKUNOVA, S.I. OLIKHOVSKII ET AL. PROC. NAP 4, 01PCSI03 (2015)   01PCSI03-2 Partial amplitudes of scattering of strong Bragg waves into diffuse ones in the diffraction direction K H  in Eq. (3) are described by:      21 2, 1 e4iK tVKF MB B     HG HGK K ,     0M c M HG G ,         0 0M c     G G HGq q ,      C δ    GG GG G G qq ,   eiK tB c    .   Here, 1C  GG  at  G G , and C C GG  at  G G , the quantities τ  are accommodations of wave vectors of diffusely scattered waves, dsi  is the absorption coeffi-cient due to DS from defects in i th type. The diffuse component of differential reflectivity of multilayered system, which is measured by triple-crystal diffractometer (TCD), can be represented as   diff ext abs diff0( ) ( )Mj j jjr F F r κ κ , (4)  where extjF and absjF are extinction and absorption factors, respectively, and two-dimensional vector κ is the momentum transfer in scattering plane. The func-tion diff ( )jr κ  represents the diffuse component of the differential reflection coefficient of j th layer integrated over a vertical divergence:    diff D1( )j y jr dk RK κ k  (5)    2 2D 0 0( )j jjR f S E Hk  (6)  Here ...j means averaging over chaotic distribution of defects in j th layer, and S is the entrance surface area of the crystal.   3. EXPERIMENT  The investigated samples had the same structure consisting of fifteen periods of {InxGa1−xAs (8 ML)/GaAs (26 ML)} with the nominal In concentration x  0.2. The diffraction profiles and reciprocal lattice maps for these samples have been measured at symmetrical (004) reflection of CuK1 radiation by using the high-resolution X-ray diffractometer PANalytical X`Pert Pro MRD XL (Fig.1 and 2).  4. RESULTS AND DISCUSSION  The quantitative analysis and reliable interpreta-tion of differential reflectivity from multilayered struc-tures require using both adequate theoretical model of diffraction and realistic model of structural imperfec-tions of these structures. The model of defect structure, which assumed the presence of randomly distributed microdefects in multilayered system, was created and applied to account for structural imperfections in mul-tilayered system. The analysis of the measured X-ray data within the framework of proposed diffraction model based on the statistical theory of dynamical X-ray scattering in im-perfect single crystals and multilayer structures [3–5] has allowed to determine parameters of strain profiles and characteristics of Coulomb-type defects in the samples. The differences in both non-uniform In con-centration profiles in the InxGa1−xAs layers (corre-sponding to self-organized QDs) and defect structures in samples have been determined for various growth temperatures.    Fig. 1 – Measured reciprocal lattice map around GaAs 004 reflection for InGa/GaAs multilayer structure grown at sub-strate temperature of 510˚C   -5000 -4000 -3000 -2000 -1000 0 1000 20001E-71E-61E-51E-41E-30,010,11-5000 -4000 -30001E-61E-51E-41E-30,012R1  Fig. 2 – Measured (1) and calculated (2) profile for GaAs 004 reflection for InxGa1−xAs/GaAs multilayer structure grown at substrate temperature of 510˚C   Fitting the experimental diffraction profiles for GaAs 004 reflection for InxGa1−xAs/GaAs multilayer structures grown at various temperatures (see Fig.2 for substrate temperature 510˚C) and analysis of ex-perimental and calculated reciprocal space maps has allowed to find more precisely thicknesses of layers and their chemical compositions, namely, fifteen peri-ods of {InxGa1−xAs (8 ML)/GaAs (26 ML)} with x  0.195. Thus, analysis of diffraction profiles and reciprocal lattice maps from multilayered structure with  InGaAs QW, which has been carried out on the basis of the developed model of dynamical X-ray diffraction by multilayered structures with defects, has allowed  DYNAMICAL X-RAY DIFFRACTION CHARACTERIZATION … PROC. NAP 4, 01PCSI03 (2015)   01PCSI03-3 for obtaining much more information about crystal and defect structure of this system as compared with results of classical diffraction models. Substantially new diagnostic opportunities have appeared due to the introduction of DS effects from defects in the dif-fraction model, what has allowed to calculate correctly the diffuse component of measured diffraction profiles and reciprocal lattice maps and to find corresponding characteristics of defects.      a  b  Fig. 3 – Calculated coherent (a) and diffuse (b) components of  reciprocal lattice map for InxGa1−xAs/GaAs multilayer struc-ture grown at substrate temperature of 510˚C   5. RESUME AND CONCLUSION  The dynamical theory of X-ray scattering by multi-layered structures with homogeneously distributed defects in each layer has been developed. The dynam-ical recurrence relation for amplitudes of coherent waves in such structures has been deduced. Expres-sions for the diffuse component of diffraction profiles and reciprocal lattice maps have been obtained with account for the redistribution of intensities of transmit-ted and diffracted coherent waves in each layer. On the basis of the derived formulas, for the first time the full and adequate analysis of diffraction profiles and reciprocal lattice maps from multilayered structure with InGaAs QDs has been performed. As result of fitting the experimental diffraction profiles and reciprocal lattice maps, thicknesses of layers, and their chemical composi-tions have been found more precisely. Additionally, char-acteristics of microdefects have been determined. The developed theoretical model of diffraction in multilayered structures with defects and the corre-sponding procedure of the self-consistent fitting the measured diffraction profiles and reciprocal lattice maps have created a basis for qualitatively new method of diffractometric diagnostics of structural characteris-tics of multilayered crystal systems with defects.   REFERENCES  1. Nano-Optoelectronics: Concepts, Physics and Devices (M. Grundmann) (Springer, Berlin-Heidelberg, 2002). 2. D. Bera, L. Qian, T.-K. Tseng, and P.H. Holloway, Materi-als 3, 2260 (2010).  3. V.B. Molodkin, S.I. Olikhovskii, E.N. Kislovskii, T.P. Vladimirova, E.S. Skakunova, R.F. Seredenko, and B.V. Sheludchenko, Phys. Rev. B. 78, 224109 (2008). 4. V.B. Molodkin, S.I. Olikhovskii, Ye.M. Kyslovskyy, I.M. Fodchuk, E.S. Skakunova, E.V. Pervak, and V.V. Molodkin, Phys. Stat. Sol. A 204, 2606 (2007). 5. S.І. Olikhovskii, V.B. Molodkin, E.S. Skakunova, E.N. Kislovskii, and I.M. Fodchuk, Phys. Stat. Sol. 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Dynamical X-Ray Diffraction Characterization of the Self-Organized Quantum Dot Formation In Imperfect Semiconductor Superlattices

Dynamical X-Ray Diffraction Characterization of the Self-Organized Quantum Dot Formation In Imperfect Semiconductor Superlattices

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