Strain distributions and electronic subband energies of self-assembled CdTe quantum wires grown on ZnTe buffer layers

Transcription

1 JOURNAL OF APPLIED PHYSICS 102, Strain distributions and electronic subband energies of self-assembled CdTe quantum wires grown on ZnTe buffer layers J. T. Woo, S. H. Song, I. Lee, and T. W. Kim a Research Institute of Information Display, Division of Electronics and Computer Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul , Korea K. H. Yoo Department of Physics and Research Institute of Basic Sciences, Kyung Hee University, Seoul , Korea H. S. Lee and H. L. Park Institute of Physics and Applied Physics, Yonsei University, Seoul , Korea Received 8 March 2007; accepted 19 June 2007; published online 15 August 2007 The structural properties and the shape of self-assembled CdTe/ZnTe quantum wires QWRs grown by using molecular beam epitaxy and atomic layer epitaxy were determined by using atomic force microscopy AFM measurements, and the interband transitions in the CdTe/ZnTe QWRs were investigated by using temperature-dependent photoluminescence PL measurements. The shape of the CdTe/ZnTe QWRs on the basis of the AFM image was modeled to be a half-ellipsoidal cylinder approximately. The temperature-dependent PL spectra showed that the PL peaks corresponding to the interband transitions from the ground electronic subband to the ground heavy-hole band E 1 -HH 1 shifted to lower energy with increasing temperature. Strain distributions and electronic subband energies at several temperatures were numerically calculated by using a finite-difference method FDM with and without taking into account shape-based strain and nonparabolicity effects. The excitonic peak corresponding to E 1 -HH 1 interband transitions, as determined from the PL spectra, was in reasonable agreement with that corresponding to the E 1 -HH 1 transitions obtained, as determined from the FDM calculations taking into account shape-based strain and nonparabolicity effects. The present results help improve understanding of the electronic structures of CdTe/ZnTe QWRs American Institute of Physics. DOI: / I. INTRODUCTION a Corresponding author; electronic mail: twk@hanyang.ac.kr Semiconductor nanostructures have been particularly attractive because of the interest in their promising applications in electronic and optoelectronic devices operating at lower currents and higher temperatures. 1 5 Potential applications of semiconductor nanostructures have driven extensive efforts to grow various kinds of nanostructures on semiconductor substrates. 6 Among the various kinds of nanostructures, quantum wells and quantum dots have been the most extensively studied structures However, relatively little work has been done on quantum wires QWRs in comparison with quantum wells and quantum dots because of the complicated processes encountered in the formation techniques. Some studies on the fabrication and the physical properties of III-V/III-V QWRs by using lithographic processes or self-assembled method have been reported In comparison with group III-V/III-V QWR structures, few works on the formation of self-assembled II-VI/II-VI QWRs have been performed. Among II-V/III-V QWR structures, the CdTe/ZnTe QWR has become particularly interesting because of its potential applications in optoelectronic devices operating in the green region of the spectrum. 16 Even though a few works on the formation and the optical properties of the CdTe/ZnTe QWR have been reported, 16 studies concerning the strain distributions and the electronic subband energies of self-assembled CdTe/ZnTe QWRs have not yet been reported because of the inherent problems encountered with the complicated computation procedure. 17 This paper reports concerning the strain distributions and the electronic subband energies of self-assembled CdTe QWRs grown on ZnTe buffer layers by using molecular beam epitaxy MBE and atomic layer epitaxy ALE. Atomic force microscopy AFM measurements were performed to determine the size and the shape of the CdTe layers grown on ZnTe buffer layers. Photoluminescence PL measurements were carried out in order to investigate the interband transitions in the CdTe/ZnTe QWRs. The strain distributions and the electronic subband energies of the CdTe/ZnTe QWRs were calculated by using a finite difference method FDM, taking into account shape-based strain and nonparabolicity effects. The theoretical interband transitions from the ground electronic band to the ground heavyhole band E 1 -HH 1 were compared with the experimental PL results. The difference between the theoretical and the experimental results could be significantly reduced by using a FDM taking into account the shape-based strain. II. THEORETICAL CONSIDERATIONS The strain fields and the electronic subband energies in the CdTe QWRs were calculated by using a FDM. When the /2007/102 3 /033521/7/$ , American Institute of Physics

2 Woo et al. J. Appl. Phys. 102, e A zz a A 0 = 1+e B xx a B 0, 1+e A yy a A 0 = 1+e B yy a B 0, 1 FIG. 1. Schematic diagrams of a the structure consisting of two neighboring meshes A and B with common x- and y-coordinates and different z-coordinates and b each normal component of the stresses on the tangential plane. orthogonal meshing is adopted, the unnecessary noises induced by the shear strain components, which are typically generated at the nonorthogonal meshing like a finite element method FEM, can be removed, and the computational complexities can be also simplified. Even though the selfconsistent convergence originating from the three band is used in this study, the main analysis was practically performed under one band approximation. Therefore, only normal strain components are required to compute a strained potential. Unevenly spaced meshing techniques were introduced to increase the computational efficiency. Since the complexity of the calculations for two- or three-dimensional nanostructures is dramatically increased, an efficient technical description of the nanostructures by utilizing a sparse matrix-storing method is required. 18 The strain effect is not typically considered in calculations of the electronic properties of lattice-matched heterostructures. 19 When the shapebased strain relations determined from the elastic continuum theory were derived, the interface of each orthogonal mesh has three relations between the normal strain components Figure 1 shows the schematic diagrams of a the structure consisting of two neighboring meshes A and B with common x- and y-coordinates and a different z-coordinate and b each normal component of the stresses on the tangential plane. For common x- and y-coordinates and a different z-coordinate between two neighboring meshes A and B, the relationships between the two tangential strain components and the one normal stress component are given by C A 12 e A xx + C A 12 e A yy + C A 11 e A zz = A xx = B xx = C B 12 e B xx + C B B 12 e yy + C B 11 e B zz, where a 0 is the lattice constant, C 11 and C 12 are the elastic stiffness constants with respect to the sample, A zz and B zz are the normal stresses of the mesh A and the mesh B, and e xx, e yy, and e zz are the normal strain components. An additional consideration for the boundary conditions is necessary if more accurate strain fields are to be achieved. Equation 1 is consistent with the following one-dimensional quantum-well strain equation: 23 a A 0 = 1+e B yy a B 0, C B 12 e B xx + C B 12 e B yy + C B 11 e B zz =0, e B xx = e B yy = a 0 A B a 0 B, a 0 B = 2C B 12 e zz B C 11 e xx B. The difference in the computational complexity between the required normal strain components and the suggested independent relations for the nanostructures can be removed by using a least-squares approximation in the numerical analysis to obtain optimized solutions. 24 The nonparabolic effective masses of the bands, which depend on the energy with a shape-dependent potential, are taken into account by using the bulk dispersion, and the electronic subband energies are calculated by using a self-consistent method with the unevenly-spaced meshing for the FDM and by taking into account nonparabolicity effects by using the physical parameters summarized in Table I and the following Schrödinger equation: 25 2 y 2 1 m y,z,e 2 y,z y + z 1 y,z + V y,z y,z m y,z,e z = E y,z. 3 When the centered finite difference expansions for the firstderivative terms are applied to Eq. 3, Eq. 3 can be recast into the following equation: y + y + + y ++,z y,z m y + y +,z,e y + + y ++ y,z y y y,z m y y,z,e y + y y + + y y,z + z + + z ++ y,z m y,z + z +,E z + + z ++ y,z y,z z z m y,z z,e z + z +. 4 z + + z

3 Woo et al. J. Appl. Phys. 102, The mean value is taken to approximate the continuities between discrete values: 26,27 m y + y/2,z,e = 1 m y,z,e + m y + y/2,z,e. 2 5 The potential energies related to the electronic parameters and the shape deformation should be included in the potential energy term in Eq. 3 : 23 V c = r E g + a c e xx + e yy + e zz, V HH = r 1 E g + a v e xx + e yy + e zz + b 2 e xx + e yy 2e zz, where V c is the edge energy of the conduction band, V HH is the edge energy of the heavy-hole band, r is the band offset ratio, E g is the energy band gap, and a c, a v, and b are the deformation potentials. III. EXPERIMENTAL DETAILS 6 The several kinds of samples used in this study were grown on semi-insulating 100 -oriented GaAs substrates by using MBE and ALE and consisted of the following structures: a 1000 Å undoped ZnTe capping layer deposited by MBE, CdTe thin films with 2.5 and 2.8 monolayers MLs deposited by ALE, and a 1 m undoped ZnTe buffer layer deposited by MBE. The depositions of the ZnTe and the CdTe layers were done at a substrate temperature of 310 C. The source temperatures of the Cd, Zn, and Te sources for the ZnTe and the CdTe epilayers were 205, 350, and 205 C, respectively. One cycle for the ALE growth was carried out by using an optimum growth process in which the Cd effusion cell was opened for 8 s, the growth was interrupted for 1 s, a Te effusion cell was opened for 8 s, and the growth was interrupted for 5 s. The deposition of the CdTe layer was done at a system pressure of approximately Torr. The detailed growth process of the CdTe QWRs is described elsewhere. 16 The PL measurements were carried out using a 75 cm monochromator equipped with an RCA photomultiplier tube. The excitation source was the 4880 Å line of an Ar-ion laser, and the sample temperature was controlled between 14 and 120 K by using a He displex system. IV. RESULTS AND DISCUSSION Figure 2 shows the AFM images of CdTe thin layers with thicknesses of a 2.5 and b 2.8 MLs grown on ZnTe buffer layers. The AFM images of the uncapped surfaces of the CdTe films deposited with thicknesses of 2.5 and 2.8 MLs on ZnTe buffer layers show that the CdTe films were deposited as CdTe QWRs with a preferential orientation along the 01 1 direction due to coalescence. 16 When the Cd and the Te molecules are adsorbed on the ZnTe buffer layer, they aggregate and form a CdTe island due to a Stranski- Krastanov growth mode resulting from the lattice mismatch between CdTe and ZnTe; 28 these islands act as seeds for CdTe QWR growth. The size of the island formed increases continuously with the addition of molecules until the island becomes a QWR. The diameters and the heights of the cores for the CdTe QWRs with various thicknesses grown on ZnTe buffer layers are summarized in Table II. The PL spectra measured at several temperatures for the CdTe/ZnTe QWRs in the 2.5 and 2.8 ML thick CdTe films are shown in Fig. 3. The PL spectra for the CdTe/ZnTe QWRs clearly show one dominant peak corresponding to interband transitions from the ground-state electronic subband and the ground-state heavy-hole band E 1 -HH 1. The broadness of the PL peaks might originate from the various sizes of the CdTe QWRs. The peak corresponding to the E 1 -HH 1 transitions in the CdTe/ZnTe QWRs shifts to lower energy with increasing thickness of the CdTe thin film. Since the energy gaps of the CdTe QWRs decrease with increasing temperature, the PL peaks corresponding to the E 1 -HH 1 transitions shift to lower energy with increasing temperature. Figure 4 shows the half-ellipse-shaped core CdTe wire with ZnTe buffer, diameter 600 Å, and height 125 Å, which was used at T=14 K to calculate the normal strain components; Figs. 4 a and 4 b show contour maps of e xx and e yy, respectively, and Fig. 4 c shows a half-cut diagram of a bird s-eye view of e zz. The computation results are visualized TABLE I. Physical parameters used in this study for the calculation of the electronic structures of the CdTe quantum wires grown on ZnTe buffer layers Refs. 25, 30, and 31. Materials Physical parameters CdTe ZnTe Effective mass m * Electrons Heavy holes Band gap E g ev at 2 K at 1.6 K at 300 K 2.28 at 293 K Lattice constant Å Spin-orbit splittings ev Elastic moduli dyn/cm 2 C C Deformation potentials ev a c a v b Band offset ratio 0.75

4 Woo et al. J. Appl. Phys. 102, FIG. 2. AFM images of CdTe thin layers with thicknesses of a 2.5 and b 2.8 ML grown on ZnTe buffer layers. by the diversified representation on graph of theoretical computations. The diameter and the height of the CdTe QWR were estimated from the AFM image. Because the electronic structures of the CdTe/ZnTe QWRs were significantly affected by the deformations of the potential energies of the conduction band and the heavy-hole band due to the lattice mismatch between the CdTe and the ZnTe layers 5.89%, 29 strain effects are considered in the calculation of the electronic subband energies in the CdTe/ZnTe QWR. The strain distribution was calculated as a function of the position by using a FDM with an unevenly spaced mesh to describe the cross-sectional structure of a single CdTe/ZnTe QWR and presenting the strain tensor in a cross-sectional plane y,z with respect to the crystal main axes. The compressive strain in the CdTe QWR was mostly formed due to the lattice mismatch between the CdTe QWR s active layer and the ZnTe TABLE II. Diameters and heights of the cores for the CdTe quantum wires with various thicknesses grown on ZnTe buffer layers used in this study for the calculation of the electronic structures. CdTe film thickness ML Observed values Å Average values Å 2.5 Diameter Height Diameter Height FIG. 3. Photoluminescence spectra measured at several temperatures for CdTe quantum wires with thicknesses of a 2.5 and b 2.8 ML grown on ZnTe buffer layers. barriers. The normal strain components obtained from this calculation were due to the shift of the conduction band and the heavy-hole band energy. Because the large strain existing at the CdTe/ZnTe hetero-interfaces induces variations in the conduction and the hole band-edge surfaces, as shown in Fig. 4, strain deformation potential effects should be considered if the exact electronic subband states of CdTe/ZnTe QWR are to be determined. Figure 5 shows the half-ellipse-shaped core CdTe wire with a ZnTe buffer, diameter 600 Å, and height 125 Å, which was used at T=14 K to calculate the strained poten-

5 Woo et al. J. Appl. Phys. 102, FIG. 5. A half-ellipse-shaped core CdTe wire with a ZnTe buffer, diameter 600 Å and height 125 Å at T=14 K, was used to calculate the strained potential: half-cut diagrams of the bird s-eye view of a the conduction band potential and b the heavy-hole band potential. FIG. 4. A half-ellipse-shaped core CdTe wire with a ZnTe buffer, diameter 600 Å and height 125 Å at T=14 K, was used to calculate the normal strain components: the contour maps of a e xx and b e yy, and c a half-cut diagram of the bird s-eye view of e zz. tial; Fig. 5 a shows a half-cut diagram of the bird s-eye view of the conduction band potential and Fig. 5 b shows a heavy-hole band potential. The strain potential energy calculated by taking into account the three kinds of normal strain components shown in Fig. 4 irregularly lifted the potential along the boundary line of the half-ellipse-shaped core, which significantly affected the E 1 -HH 1 interband transitions. Figure 6 shows the excitonic peaks corresponding to the E 1 -HH 1 transitions in the CdTe/ZnTe QWR determined from the temperature-dependent PL spectra and the theoretical results related to the E 1 -HH 1 transitions calculated by using a FDM with and without considering the strain effects. The E 1 -HH 1 transition energies in the CdTe/ZnTe QWR calculated by using the FDM taking into account the strain effect are shifted by up to approximately 600 mev in comparison with those of the CdTe/ZnTe QWR calculated by using the FDM without considering the strain effects, as shown in Fig. 6. The temperature dependency of the E 1 -HH 1 transition energy is largely due to a decrease in the energy band gap of the CdTe and ZnTe with increasing measurement temperature. The E 1 -HH 1 transitions in the CdTe/ZnTe QWR, as determined from the PL spectra, are in reasonable agreement with those calculated by using the FDM taking into account strain effects. The small deviation might originate from the exciton binding energy of the CdTe/ ZnTe QWR, which is not considered in this calculation, even though more accurate electronic subband energies have been calculated by using the FDM and taking into account strain effects together with nonparabolicity effects. Figure 7 shows that half-cut diagrams of the bird s-eye views for a the electron ground-state probability density function at the conduction band calculated by using a FDM without considering of the strain effect, b the deformation energy of the conduction band potential due to the strain effect, and c the electron ground-state probability density function at the conduction band calculated by using a FDM taking into account the strain effect. A half-ellipse-shaped core CdTe wire with a diameter of 600 Å and a height of 125 Å grown on a ZnTe buffer layer at T=14 K was used to calculate the probabilistically electronic confinement. The quantum confinement of the electrons in the half-ellipseshaped core on the cross-sectional plane of the CdTe QWR without considering the strain effect is probabilistically shown in Fig. 7 a. The confinement distribution of the electrons around the center of the cross-sectional plane of the CdTe QWR is described in Fig. 7 a. A band edge potential profile with respect to the energy band parameters has a cylindrical shape on the cross-arsectional plane of the CdTe QWR without considering the strain effect. The electronic transition energies are dependent on the temperature, corresponding to the dashed line shown in Fig. 6 b, which is significantly different from the PL results. When the deformation potential energy described in Fig. 7 b is considered, the potential profile shown in Fig. 5 a can be obtained, and the calculated transitions energies indicated by the solid line in Fig. 6 b are in reasonable agreement with the PL results. The probabilistic distribution of the electron confinement is shown in Fig. 7 c. The deformation potential energy on the sectional plane of the CdTe QWR has the linear behavior similar to that of the QW at the straight boundary line, and the deformation potential energy significantly increases to

6 Woo et al. J. Appl. Phys. 102, FIG. 7. Half-cut diagrams of the bird s-eye views for a the electron ground-state probability density function at the conduction band calculated by using a FDM without considering the strain effect, b the deformation energy of the conduction band potential due to the strain effect, and c the electron ground-state probability density function at the conduction band calculated by using a FDM taking into account the strain effect. A halfellipse-shaped core CdTe wire with a diameter of 600 Å and a height of 125 Å grown on a ZnTe buffer layer at T=14 K was used to calculate the probabilistically electronic confinement. FIG. 6. Comparison of E 1 -HH 1 interband transitions between experimental PL and theoretical results at several temperatures for CdTe quantum wires with thicknesses of a 2.5 and b 2.8 ML. Solid circles represents the experimental E 1 -HH 1 interband transition data, and solid and dashed lines indicate the theoretical results calculated with and without taking into account strain and nonparabolicity effects, respectively. the concentrated point due to the two-dimensional distortion at the nonlinear boundary. Because the deformation of the strain significantly increases along the concave boundary, the confinement probability of the electrons around the center of the straight boundary increases, resulting from the contraction of the band edge potential of the barrier due to an increase in the strain deformation. V. SUMMARY AND CONCLUSIONS Strain distributions and electronic subband energies at several temperatures were numerically calculated by using a FDM with and without taking into account shape-based strain and nonparabolicity effects. The experimental E 1 -HH 1 interband transitions for self-assembled CdTe/ ZnTe QWRs, as determined from the temperature- and structure-dependent PL spectra, were in reasonable agreement with the theoretical E 1 -HH 1 transitions calculated by using a FDM taking into account shape-based strain effects. The PL peaks corresponding to the E 1 -HH 1 interband transitions shifted to lower energy with increasing temperature, which was in reasonable agreement with the theoretical E 1 -HH 1 transitions. The present results indicate that the strain effects play an important role in determining the electronic subband energies of CdTe/ZnTe QWRs. These results can help improve understanding of the strain distributions and the electronic subband energies of CdTe/ZnTe QWRs. ACKNOWLEDGMENT This work was supported by the Korea Research Foundation Grant funded by the Korean Government MOEHRD, Basic Research Promotion Fund Grant No. KRF J S. A. Empedocles and M. G. Bawendi, Science 278, Y. Toda, O. Moriwaki, M. Nishioka, and Y. Arakawa, Phys. Rev. Lett. 82, Y. J. Doh, J. A. V. Dam, A. L. Roest, E. P. A. M. Bakkers, L. P. Kouwenhoven, and S. D. Franceschi, Science 309, C. Yang, Z. Zhong, and C. M. Lieber, Science 310, P. J. Pauzauskie, A. Radenovic, E. Trepagnier, H. Shroff, P. Yang, and J. Liphardt, Nat. Mater. 5, D. D. Vvedensky, in Low-dimensional Semiconductor Structure, edited by K. Barnham and D. Vvdensky Cambridge U. P., Cambridge, 2001, Chap B. Aneeshkumar, A. Yu. Silov, M. R. Leys, and J. H. Wolter, Appl. Phys. Lett. 83, D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M. Petroff, Appl. Phys. Lett. 63, V. Ustinov and E. R. Weber, Appl. Phys. Lett. 72, T. M. Hsu, W.-H. Chang, C. C. Huang, N. T. Yeh, and J.-I. Chyi, Appl.

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