Cobet, Christoph

Esser, Norbert

Goldhahn, Rüdiger

Rakel, Munise

Richter, Wolfgang

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     Rakel, Munise; Cobet, Christoph; Goldhahn, Rüdiger; Richter, Wolfgang; Esser, Norbert; VUV-XUV Dielectric Function of InN  Zuerst erschienen in: Highlights / Annual report 2004 // Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung m.b.H. - Berlin : BESSY, 2005, S. 413-415.  Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung m.b.H.BESSY - Annual ReportBESSY GmbH • Mitglied der Leibniz-Gemeinschaft (WGL)  • Vorsitzender des Aufsichtsrates: Prof. Dr. Joachim Treusch, JülichGeschäftsführer : Prof. Dr. Dr. h. c. Wolfgang Eberhardt, Prof. Dr. Eberhard Jaeschke • Sitz der Gesellschaft : Berlin •Handelsregister : Amtsgericht Charlottenburg HRB 14 635  • Bankkonto: Deutsche Bank  AG, Filiale Berlin, Konto-Nr. 4 173 001 01, Bankleitzahl 100 700 00Published by:Berliner Elektronenspeicherring-Gesellschaftfür Synchrotronstrahlung m.b.H. (BESSY)Albert-Einstein-Str.1512489 BerlinTel. +49 30 6392 2999Fax +49 30 6392 2990 info@bessy.dewww.bessy.deEdited by :Dr. Kai GodehusenVUV-XUV Dielectric Function of InNM. Rakel1,3, C. Cobet1,3, R. Goldhahn2, W. Richter1 and N. Esser31Institut fu¨r Festko¨rperphysik, TU Berlin, Hardenbergstr. 36, D-10623 Berlin2Inst. f. Physik, Zentrum f. Mikro- und Nanotechnologien, TU Ilmenau, D-98684 Ilmenau3ISAS- Institute for Analytical Sciences, Albert-Einstein-Str. 9, D-12489 BerlinBMBF (DESY): 05 KS4KTB/3An ellipsometric study on InN and GaN in a spectral region from 2.5 till 30eV is presented.These nitrides crystallize in the thermodynamically stable wurtzite (hexagonal) structure and inthe metastable zinc blende (cubic) structure. Especially for InN relatively few experimental studiesof the optical properties have been carried out although the recently found small band gap value of0.7 eV increases the possible emission range of III-nitride optoelectronic devices from the deep UVdown to the near IR region. A further advantage of InN is the small electron effective mass whatleads to a large saturation velocity. That makes InN to a promising material for high speed or highfrequency electronic devices.By taking advantage of using linear polar-∆Figure 1: The imaginary parts of the ordinary εo2 and ex-traordinary εe2 DF of a-plane InN in the spectral range ofinterband transitions.ized light in an ellipsometric measurement,the dielectric tensor components correspond-ing to the electric field vectors along the crys-tallographic axes, can be separately exam-ined. This allows a separation of directiondependent electronic contributions and thusa study of the anisotropy of the chemicalbondings. In particular for the wurtzite struc-ture (coordination number 4) the anisotropyin the chemical bonds along the c axis andin the plane (slightly tilted with respect tothe c plane) defines the amount of opticaltransitions in different directions. For the el-lipsometric investigation of this anisotropicelectronic properties hexagonal samples arerequired for which the c-axis lies in the sur-face plane, like in m-plane GaN (1-100) and a-plane InN (11-20). As recently reported in Ref. [6]one succeeded in depositing high quality a-plane InN on r-plane sapphire with an AlN nucleationand GaN buffer layer using plasma assisted MBE. By use of these samples measurements of thedifferent components were realized by rotating the sample in the two high symmetry orientationswere the optical axis is either parallel or perpendicular to the plane of incidence.The ordinary and extraordinary dielectric function (DF) where determined the first time withthe BESSY ellipsometer at the 3m-NIM-monochromator in the spectral range above the commonband gap of about 0.7 eV [4, 5]. The imaginary parts of both components (Fig. 1) show remarkabledifferences. While for the ordinary component at least seven absorption structures at 4.82, 5.38,6.18, 6.54, 7.66, 7.94 and 8.54 eV contribute to the DF, we can identify only three at 5.40, 7.61 and9.16 eV in the extraordinary component up to 10 eV . Furthermore, correlated absorption peaksdiffer in the magnitude and are shifted in their energy against each other. A heuristic assignmentof the different structures can be found in comparison with earlier results on wurtzite-type GaN [3]and CdS or CdSe [1]. Within this assignment the cubic E1 transitions are understood in terms ofcritical points (CP) or lines along the ±[111] directions of the corresponding zinc-blende Brillouin413⊥εFigure 2: Imaginary part of the hex. GaN ordinary DFin comparison with the DOS of p-like conduction bands(DFT-LDA [7]). The energy position of the DOS wascalculated in relationship to the Ga3d-core states andshifted by 1.5 eV.⊥εεFigure 3: Third derivative of the ordinary DF of thehex. GaN. Both Ga3d valance band transitions struc-tures show distinct a spin-orbit splitting of 0.41 eV.zone. In the cubic crystals, these states are degenerated with the corresponding stats in the ±[111],±[111], and ±[111] directions. The symmetry of the ±[111] directions are very similar to that of thecorresponding ±[0001] c axis of wurtzite crystals, while the other three split in wurtzite structuresfrom ±[111] but remain degenerate with each other due to the sixfold symmetry around the caxis. Together with the corresponding cubic E’0 CP this two CP’s can be attributed to the threeabsorption structures at 4.82, 5.38, 6.18 eV in the ordinary component. A symmetry considerationindicates that the [111]-like singlet appears only for ε‖ while the ±[111] triplet should appear forboth polarizations. According to this interpretation, the measured extraordinary component showsonly one strong absorption structure at 5.40 eV where the ±[111] triplet is found degenerated withthe E’0 transitions. Within this argumentation the following two major absorption structures in theordinary component of the DF can be attributed to the cubic E2 (located along the ±[111] direction)and E’1 CP’s. But in the hexagonal crystal structure no associate high symmetry axis could berelated to the cubic ±[111] direction. Consequently, the correlated hexagonal InN E2 CP’s are foundin both components of the DF while the E’1 CP is showing again a strong anisotropic behaviour.But, in the limitation of the presented spectral range no comparable splitting in the ordinarycomponent is found like for the E1 transition. Anyhow, discrepancies beyond the pure symmetryargumentation can be attributed to anisotropic chemical bonds parallel and perpendicular to the caxis.In a spectral region above 15eV the DF of GaN and InN is dominated by optical transitionsbetween the Ga3d/In4d semicore and the p-like unoccupied (conduction) electron states. Becauseof the nondispersive behaviour of the d-band one gets a characteristic view of the p-like conductionbands. The electron transition is governed by the dipole selection rules what results in the fact,that a d electron can only be excited to p- or f-orbital. In the case of c-plane GaN the DFT-LDAcalculations for the p-like DOS are fitting into the experimental spectra what is shown in Fig. 2.With a resolution better than 0.02eV we find also evidences for the predicted spin-orbit splitting ofthe d-bands. Similar to the theoretical predictions or photo emission measurements we determinea spin-orbit splitting of 0.41 eV for GaN (Fig. 3). In Fig. 4 the DF of a-plane InN is shown for bothcomponents. From the pure symmetry argumentation no principle differences are expected betweenthe hexagonal ordinary and extraordinary or the cubic DF. But the two measured components differconsiderable in the principal line shape and emphasis the assumption of a large anisotropy in thechemical bonding. For the In4d levels a somewhat higher spin-orbit splitting is predicted than forGaN. Possibly, this is not resolved due to the low crystal quality of the available samples.414For the XUV-measurements (12-30eV) the TGM-4 beamline was used as light source.⊥⊥Figure 4: Imaginary parts of the ordinary εo2 and ex-traordinary εe2 effective DF of a-plane InN in the spec-tral range of the In4d excitations.⊥εFigure 5: Imaginary part of the ordinary εo2 DF func-tion of c-plane InN at different temperatures.Finally VUV ellipsometric measurements were also taken on c-plane MBE grown InN (1070 nmlayer thickness) at the 3m-NIM1 beamline. It is assumed that InN forms a native oxide on the surfaceand is highly water contaminated while leaving it in air atmosphere. In order to get rid of thesecontaminations, the sample was annealed at 480◦C for 10 min in UHV. This kind of ”deoxidation”yields to a considerable change in amplitudes like shown. For temperature dependent investigations,spectra were taken between 440 K and 160 K. Fig. 5 shows a comparison with the room temperaturespectra. Like expected there is a blue shift for the low and a red energy shift for the high temperaturestructures, whereas the low temperature spectra has a much sharper quality. After first and secondderivation analysis under consideration of the Kramers-Kronig consistency we can clearly verifyseven interband transition peaks for energies till 10eV as discussed above. But surprisingly, weobserved remarkable variations in the amplitude behaviour for the different interband transitions,especially for the structure at 8.6 eV. The latter shows a much stronger increase of peak height withdecreasing temperature than the other structures. A closed cycle cryostate will be mounted in thefuture in order to enhance interband transition structures and to resolve the predicted anomalousspin-orbit splittings of the top valence bands [2].[1] M. Cardona. Solid State Communications, 1:109, 1963.[2] M. Cardona and N. E. Christensen. Solid State Communications, 116(8):421, 2000.[3] C. Cobet, N. Esser, J. T. Zettler, W. Richter, P.Waltereit, O. Brandt, K. H. Ploog, S. Peters, N. V. Edwards,O. P. A. Lindquist, and M. Cardona. Phys. Rev. B, 64:165203, 2001.[4] R. Goldhahn, V. Cimalla, O. Ambacher, C. Cobet, W. Richter, N. Esser, H. Lu, and W.J. Schaff. BESSYJahresbericht, pages 377–379, 2003.[5] R. Goldhahn, A. T. Winzer, V. Cimalla, O. Ambacher, C. Cobet, W. Richter, N. Esser, J. Furthmu¨ller, F. Bech-stedt, H. Luf, and W. J. Schaff. Superlattices and Microstructures, 36:591–597, 2004.[6] H. Lu, W. J. Schaff, L. F. Eastman, J. Wu, W. Walukiewicz, V. Cimalla, and O. Ambacher. Appl. Phys. Lett.,83(6):1136–1138, 2003.[7] W. G. Schmidt, 2004. Institut fu¨r Festko¨rpertheorie und -optik, Friedrich-Schiller-Universita¨t Jena, Germany,priv. com.415

VUV-XUV Dielectric Function of InN

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VUV-XUV Dielectric Function of InN

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