Structural properties, Interface Modes and Magnetophonon Resonances. in the Double Quantum Well structure

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1 Structural properties, Interface Modes and Magnetophonon Resonances in the Double Quantum Well structure D. Płoch 1, T. Płociński 2, W. Gębicki 3, E.M. Sheregii 1 and K.J. Kurzydłowski 2 1 University of Rzeszow, Centre of Microelectronics and Nanotechnology, Rejtana 16a, Rzeszow, Poland 2 Warsaw University of Technology, Faculty of Materials Science and Engineering, ul. Wołoska Warsaw 3 Warsaw University of Technology, Faculty of Physics, ul. Koszykowa Warsaw Abstract The results of investigations of the Double Quantum Well structure (DQWs) of special engineering are reported. The Scanning Transmission Electron Microscopy (STEM) observations confirmed a high quality of interfaces and smooth change of the In-content in a rectangular shape QW. Micro-Raman experiment enabled to detect interface phonons in DQWs which are manifested in Magnetophonon Resonance. This contribution of interface phonons in the electron magneto-transport is important because as could be expected, the role of these phonons will increase in case of electron transport in the Double Quantum Wires fabricated from DQWs investigated. PACS: Ja, Fs Introduction Double Quantum Wells structures (DQWs) attract attention because of their potential for quantum computing [1-3]. Electrons in the DQWs are occupying symmetric and anti-symmetric states allowing for flying quibits in Double Quantum Wires with ballistic transport of electrons [3]. As was shown in our previous papers [4-6] the electron system in the DQWs is divided on two sub-systems with symmetric and anti-symmetric states, weakly interacted at low temperatures (lower than 10 K) because of the transitions between these states due to electron-electron interaction (e-e) being forbidden. It implies that phonon spectra and electron-phonon (e-p) interactions in the DQW are important at temperatures above 77 K and should be investigated carefully. The Raman scattering and Magnetophonon Resonance are excellent method to study these phenomena in the semiconductor structures. An important aspect is also quality of DQWs which determines parameters of 2DEG as 2Dreservour for ballistic transport in the Quantum Wires. The results of complex investigations of DQWs of special engineering provided the rectangular shape of QW, are presented in this paper. The Scanning Transmission Electron Microscopy (STEM), Raman scattering and Magnetophonon Resonance enable us to estimate the quality of the researched structures and the role of the interface phonons in the electron magneto-transport. Description of DQWs The InGaAs/InAlAs/InP DQWs were grown by low pressure metalorganic vapor phase epistaxy (LP-MOVPE) on semi-insulating (100) InP:Fe substrates. The process is in detail described in [7] for case of single quantum well structures and certain data about the DQW growth process are presented below. A horizontal quartz reactor (AIX-200R&D) and IR heated graphite sucseptor were used.

2 Trimethylgallium (TMGa), trimethylindium (TMIn), trimethylaluminum (TMAl) and arsine AsH 3, phosphine PH 3 were used as III and V group element precursors with palladium-purified hydrogen carrier gas. SiH 4 was used as a precursor for n-type doping. The reactor pressure and temperature were maintained at 100 mbar and at 650 O C, respectively, during the unstrained layer growth. The V/III ratio was unchanged and amounted to 329 for InP, 1040 for In 0,52Al 0,48As (buriers) and 198 for In 0,65Ga 0,35As (QWs). The partial pressure of SiH 4 provided doping level about cm -2. The obtained structures consisted of (from bottom to the top) an undoped 180 nm InP buffer followed by 400 nm InAlAs buffer layer on InP:Fe substrate. A delta-doping Si donor layer and 3 nm In 0,52Al 0,48As spacer were grown on each InAlAs barrier layer. The In-content in the InGaAs channels was varying from 53 to 65% during the time of 25s (about 4.75 nm). In content of 65% in the 6 nm InGaAs layer was kept constant and graded layer (from 65% to 53%) was repeated. After that, 3nm In 0,52Al 0,48As spacer, delta-doping Si donor layer and the next QW and barrier are repeated. The 25nm In 0,52Al 0,48As Schottky layer completed the structure. Fig. 1. The profile of the conduction band edge of QW. The dotted lines are the hypothetic courses shown the conduction band profile for unchanged composition of indium in the well: higher for contain of 53% of In and lower for contain of 65% of one. Thin lines show how would change the edge of conduction band without presence of Coulomb interaction between electron in QW and -doping layer. The bold line is the summarize dependence. In order to improve the quality of the layers, the growth rate and temperature of the 6 nm In0,65Ga0,35As active layer were lowered and equal to 4.1Å/s and 600 O C, respectively. The forecasted profile of conduction band edge for QW is shown in Fig.1. This profile was computed using the results by Zawadzki and Pfeffer [8] for QW of In 0.52Al 0.48As/ In 0.53Ga 0.47As. It is expected that by decreasing of conduction band edge due to increased In content in the channel from 53 to 65% over 4.75 nm compensates exactly the Coulomb interaction with ionized donors in -doping layers. Hence, the band profile from left and right hand of the In 0,65Ga 0,35As layer is horizontal. Therefore, the shape of QW is practically rectangular as the bulge in the middle is not essential (about 5 mev). Due to flat edge of QW it whole width corresponds to x=0.65 regardless of variable composition because of constant value of the energy gap: E g=0.723 ev at 77 K. The STEM results

3 Sample microstructure was examined by using Cs corrected STEM (Hitachi HD2700) at accelerating voltage of 200kV. For the sample observations were used two signals, bright field STEM (BF-STEM) and atomic mass contrast (ZC-STEM). The combination of these two signals can gave better overview on the sample structure. The EDX spectrometer was used to perform chemical element distribution in the cross section of the DQW. The sample for the investigations was prepared by using Focus Ion Beam system with lift out technique. The sample were placed on the support element and then thinned to around 100 nm thickness. In Fig.2 is shown the cross-section of DQWs with low magnification. Two QWs are clearly manifested by bright contrast on the ZC image located on the right part of this image. Three barriers are visible as more dark layers as well as the top layer and buffer are well resolved. * 0 * 1 * 2 * 3 * 4 * 5 * 6 Fig.2. The STEM picture of the DQWs cross-section. Left part corresponds to the BF-STEM signal, right side corresponds to ZC contrast. The experimental locations of the laser spot where Raman scattering data were collected, are shown by squares with numbers. Higher magnification of the two layers was presented on the Fig.3. This image has shown the thickness homogeneity of the QW layers along the sample. Two types signal combination were used to shown the layers thickness. FFT of the BF-STEM image represented <111> zone axis were added to the image. Measured values of the QW layers thickness is equal to nm and is close to the value predicted by technologists. On the image can be observed some small differences in the contrast, which can be recognized as the radiation defect introduced to the material, during sample preparation by using Ga ions beam. The high-resolution picture of QW presented in the Fig.4. enables us to estimate the quality of interfaces. The interface high quality is confirmed up to two atomic layers differences in the thickness.

4 Some changes in the brightness from the left to right side are according to change in the composition on the edge. Fig 3. The STEM picture, combined from two signals; left side is BF-STEM and right side is ZC-STEM. In upper left corner were presented Fast Fourier Transform (FFT) of the BF-STEM image. On the ZC- STEM image, were measured thicknesses of the QWs layers. Fig 4. Interface of the QW layer presented on the HR-STEM image, obtained by using HAADF detector.

5 In Fig. 5 are presented results of X-ray microanalyse performed across one of QW layer. The deep-profiles of four atoms As, In, Ga and Al enable us to verify the atom concentrations forecasted by technologists. The total concentration of Ga and In atoms in QWs is equal approximately to 50 % but increase of In-atom content is more slow what confirm the predicted change of this content at interface in QWs. The resolution of EDX analysis in thin samples has some limitations, so obtained results are on the edge of the spatial resolution of this technique. Fig.5. The results of the X-ray line scan microanalyses performed across QW-layer. Nevertheless, we can conclude that above presented results of X-ray microanalyses as well as of STEM imaging confirm the technologist s forecasting expressed by the conduction band profile shown in Fig. 1. The Raman scattering results Raman scattering spectra were measured using Reinshow Raman spectrometer and AFM microscope Ntegra. The 633 nm and 514 nm laser excitation lines were used. The micro-raman measurements were performed in backscattering geometry. The incoming light was focused across the sample cross section edge. In order to collect Raman spectra with the resolution of 1.5 cm 1 in 6 different locations chosen on a line on top of the cross-section of sample at a distance of 0.1 m each (see Fig. 2).This geometry gives a possibility to study the Raman signals coming from different layers of the quantum well structure visualized at Fig. 2. A series of Raman spectra across the sample edge are presented at Fig. 6.

6 Intensity Raman shift [cm -1 ] Fig.6. Raman spectra along the line on the cross-section shown in Fig. 2. Basically two groups of Raman bands can be distinguished on spectra shown in Fig.6. The first one below 400 cm -1 should be attributed to the longwavelength optical phonons (in the region 200 cm cm -1 ) and disordered activated acoustic phonons (in the region 100 cm cm - 1 ) from the high phonon density region of the Brillouin zones of the substrate and DQW s layers InGaAs TO? 4 - InAlAs LO Intensity [counts] InAlAs 2 - InP TO 1 - InP LO 3 - InAlAs LO Raman shift [cm -1 ] Fig. 7. The identification of the first order Raman bands shown in Fig. 6 on curves 2,3, 4 and averaged for the region 100 cm cm -1. The next group of Raman peaks above 600 cm -1 reflects the second order Raman spectra of the InP substrate. In Fig. 7 the first order Raman bands are identified. Comparison of the Raman data shows that the peaks 1 and 2 presented in the spectra shown in Fig. 7 are observed in the spectra presented in Fig. 6 when the light spot is centered at the narrow quantum wells region as well as when it is centered at the InP substrate or buffer InP layers. This observation enables to identify the Raman peaks 1 and 2 at Fig. 7 as TO and LO phonons of the InP substrate. The TO phonon frequency is in good agreement

7 with the literature results but the InP LO phonon frequency is shifted to the lower frequency the literature data on the frequency of the bulk InP LO phonon mode is 351 cm -1 [9,10,11]. The measured phonon LO phonon frequency is approximately 345 cm -1 as presented at Fig. 7 and are undoubtedly related to the InP layers. The band 3 is assigned to AlAs-like mode of InAlAs barier (phonon frequency 367 cm -1 coincides with the literature value [12]. The broad band centered approximately at 228 cm -1 (band 5) is at least a combination of two peaks i.e. InAs-like TO (226 cm -1 ) and LO InAs-like: 231 cm -1 (it is possible to expect that really that is combination of four mode: two TO InAs-like ones at 224 cm -1 and 226 and two LO InAs-like ones at 231 cm -1 and 233 cm -1 belonging to QW In 0,65Ga 0,35As and to barrier In 0,52Al 0,48As, respectively) which are resolved clearly. Nevertheless, following [12] the observed broad band could be interpreted as a combination not three but several Lorentzian bands i.e. despite InAs-like TO and InAs-like LO, the GaAs-like TO (255 cm -1 ) and GaAs like LO (268 cm -1 ) modes are contributed in this band too. An additional band centered at 244 cm -1 takes place between TO and LO InAs-like modes and could be interpreted as mode situated at the InGaAs/InAlAs interface [10] 1. The band 6 at 190 cm -1 is situated below any optical phonon frequency of the examined layers and can be interpreted as activated acoustic phonons in one of the semiconductor layers probably InGaAs [13]. Magnetophonon Resonance In case of 2D-DQW s, electrons are moving in multi-mode medium of not less than two channels: two QWs limited (separated) by barriers. As it was shown above except bulk phonons, the surface or interface can generate a phonon mode too. So, considerable number of the phonon modes characterize the phonon sub-system in DQWs. This peculiarity of phonon sub-system should be rearranged on electron transport in DQWs as diversification of electron-phonon interaction and could be appeared in Magnetophonon Resonance (MPR) as additional series of peaks [5]. Electron interacting with distinguished potentials generated by these modes, can absorb the phonon energy corresponding to the separate oscillation frequency in multi-mode lattice depending on resonance situation of the electron sub-system, e.g. resonance condition: ' E E LOs (1) where E and E are the Landau Level (LL) energies of the final and initial electron states, respectively. The MPR-experiment was performed at the galwanomagnetic measurements in the pulse magnetic fields, generated in the optimal coil build-up [15], with capacitor 10mF, 3000 Volt, energy 45kJ (duration of pulse 14ms). The transverse magnetoresistance xx(b) as a function of the magnetic field was registered up to 40 T at different temperatures within the range of K. To determine the oscillated change of magnetoresistance xx(b) in magnetic field, the background was deducted and the oscillation part of magnetoresistance was separated. 1 This interface mode was assigned as IF 1 in [11] where were researched Raman spectra of the (InP) 5 (In 0.49 Ga 0.51As) 8 superlattice

8 Fig.8. The oscillation part of magnetoresistance xx(b) for DQWs investigated obtained at temperature 77K. The MPR oscillations connect two sub-systems of crystal or low-dimensional structure (LDS) electrons and phonons which are two main excitations in lattice. Therefore, the theoretical aspect of MPR in DQW concern two questions: electron sub-system in external magnetic field Landau quantization 2DEG in our case of DQWs and interaction of conductive electrons with phonon-subsystem. The electron energy spectrum in DQW investigated is researched in detail in work [6] by optical and magneto-spectroscopy methods. The values of the sub-bands energies as well as symmetric and antisymmetric splitting (SAS-gap) were determined experimentally (Table II in [6]). It was difficult to explain why the results of the energies of the states and of the SAS-gaps for the DQW obtained in previous calculations and the energy values obtained by these optical measurements addresses a difference of about 20 %. A result that can be explained non-adequate value of QWs width introduced in the numerical calculations regarding the state energies of real rectangular QWs. The STEM results enable us to introduce adequate width of QW nm. The model presented in [5] enable us to calculate the Landau Levels (LL) energies in DQWs with both rectangular and triangle shape of QW. In Figures 9 are shown the calculated the LL energies (the E ( ) ) curves for tree sub-bands and symmetric and anti symmetric states for DQWs investigated B i, s( as), n presuming rectangular shape of the QWs with width nm. The Fermi level energy is 190 mev as it derived one from Quantum Hall Effect and Shubnikov-de Haas oscillations [4,6].

9 Fig.9. MPR with electron transitions assisted by four kinds of phonons for DQWs investigated with rectangular shape of QW. The Raman scattering results enable us to use the adequate values of the LO-phonon energies participated in the MPR. These values are presented in the Table 1. Table 1. The LO phonon frequencies and energies in QWs and barriers of researched structure 1 Lp. Structure E [mev] [ ] LO cm 1 GaAs-like in In0,65Ga0,35As QW ,23 2 InAs-like in In0,65Ga0,35As OW ,64 3 InAs-like in In0,52Al0,48As barrier ,89 4 AlAs-like in In0,52Al0,48As barrier ,78 5 InAs-like interface ,25 From Table 1 result in that five kinds of LO-phonons should be taken into account at MPR interpretations in In 0.65Ga 0.35As/ In 0.52Al 0.48As QWs. Practically that are four kind because the energies of InAs-like LO-phonons in QW and in barrier are very close. These four values of the LO-phonon energies are shown in Fig. 9 as shown the electron transitions among LLs with absorption of four kinds of phonons for DQWs with rectangular shape of QWs which are the DQW investigated. The oscillation curves of MPR are presented here too. It is seen that a group of electron transitions with absorption of

10 mentioned above four kinds of LO-phonons corresponds to each MPR peak. The dominate contribution of the InAs-like LO-phonons, belonging both QW and barriers, can be established confidently. The interface InAs-like phonons contribute in the MPR peaks and this contribution is resolved clearly. These three kind of InAs-like LO-phonons determine the main peaks of observed MPR-oscillations. Some of shown electron transitions crossed not the Fermi level and it seen that their contribution in resonance peaks is minor. Discussion and conclusions The results obtained by the STEM of the DQW investigated as well as the Raman researches and MPR experiment are consistent and explicitly indicate on high quality of structure investigated. From other hand the predictions of technologists are confirm also: the rectangular shape of QWs in DQWs is realized due to special engineering: the model of the LL energies calculation derived for rectangular shape of QWs in DQWs agree perfectly with MPR experiment after introducing the adequate width of QWs determined experimentally by STEM and using of the LO-phonon energies values which were measured by micro-raman experiment. The values of the energy states in DQW obtained by optical experiment in previous work [6] are justify by theoretical calculations after introducing the adequate value of the QW width. The micro-raman experiment enable us to distinguish the interface phonons in phonon spectra of DQW investigated (that one were find in the Raman experiment by another authors [11]) what enable us to find the contribution of the interface InAs-like LO-phonon in the MPR. This contribution in the electron magneto-transport is important because the role of these phonons as could be expected, will increase at decreasing of the dimensionality: in case of electron transport in the 1D Double Quantum Wires fabricated from DQWs investigated the electron scattering on surface (interface) phonons undoubtedly will increase. References [1] S. F. Fischer, G. Apetrii, U. Kunze, D. Schuh, and G. Abstreiter, Magnetotransport spectroscopy of spatially coincident coupled electron waveguides. Phys. Rev. B 71, (2005). [2] S. F. Fischer, G. Apetrii, U. Kunze, D. Schuh, and G. Abstreiter, Nat. Phys. 2, 91 (2006). [3] A. Bertoni, P. Bordone, R. Brunetti, C. Jacoboni, S. Reggiani, Phys. Rev. Lett. 84, 5912 (2000) [4] M. Marchewka, E.M. Sheregii, I. Tralle, D. Ploch, G. Tomaka, M. Furdak, A. Kolek, A. Stadler, K. Mleczko, D. Zak, W. Strupiński, A. Jasik, R. Jakiela, Physica E, 40, , (2008) [5] D. Płoch, E.M. Sheregii, M. Marchewka, M. Woźny and G. Tomaka, Phys. Rev. B 79, (2009) [6] M. Marchewka, E.M. Sheregii, I. Tralle, A. Marcelli, M. Piccinini and J. Cebulski, Phys. Rev. B 80, (2009) [7] G. Tomaka, E.M. Sheregii, T. Kkol, W. Strupinski, R. Jakiela, A. Kolek, A. Stadler, K. Mleczko, Cryst. Res. Tech. 38, 407 (2003) [8] W. Zawadzki and P. Pfeffer, Proc. NGS 10 IPAP Conf. Series 2, 2001, pp [9] E. Bedel, G. Lands, R. Carles, J. P. Redoules and J. B. Renucci,, J. Phys. C. Solid State Phys. 19, 1471 (1986)

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