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2009 SEMICONDUCTORS AND NANOSTRUCTURESCyclotron effective mass measurements in Indium NitrideAmong the group III-nitride materials, the electronic structureof InN is matter of continuing debate despite significantprogress during the last decade in understandingthe band structure, as the revision of its band gap energyfrom 1.8 − 2.1 eV to 0.7 eV. So far, band parameters aremostly derived from indirect methods of limited accuracysuch as infrared reflectivity measurements. For instance,the values of the effective mass remain scattered in a widerange from 0.044 m 0 to 0.093 m 0 . Moreover, a stronglyanisotropic electronic structure of the bulk crystal has beenclaimed to explain Shubnikov-de-Haas (SdH) oscillationsand magneto-optical properties. To date, the synthesis ofhighly pure InN single crystals remains a challenge and, inaddition, most measurements are affected by the presenceof an intrinsic low mobility surface and/or interface electronaccumulation layer that opens parallel conduction channels.an isotropic electron-LO phonon coupling constant in InN,α = 0.22, the polaron mass ism ∗ P = m∗ P= (1 + α/12)/(1 − α/12). (10)m∗ One finds a 4% correction that finally gives the bare massat the bottom of the conduction band equal to m ∗ 0 = 0.055±0.002 m 0 . The band parameter E p in the dispersion relation(1) thus becomes E p = 12 eV , with E g = 0.69 eV.We have recently performed the first measurement of thebulk electron cyclotron effective mass by Landau levelsspectroscopy: the most direct approach to measure effectivemasses. To derive the mass, we have used the temperaturedependence of the SdH oscillation amplitudes measuredunder magnetic field up to 60 T in the temperaturerange 2 − 70 K. A set of InN samples 1 µm thick havingHall concentrations 2 − 3 − 6 × 10 18 cm −3 has been investigated.We found an isotropic electron cyclotron effectivemass equal to 0.062 ± 0.002 m 0 but the highest doped sampleexhibits a puzzling anisotropy.In the present study, we find a single SdH series (see figure58) for magnetic field parallel to the c-axis in contrastwith [Inushima et al, Phys. Rev. B 72, 085210(2005)] where an additional SdH series at higher frequencyis reported for a sample with a similar Hall concentrationn H = 2.2 × 10 18 cm −3 . Our single series behaves like themain series of this previous study and keeps the same periodwhen the magnetic field is tilted towards a direction perpendicularto the c-axis. Consequently, this series accounts foran isotropic bulk Fermi surface as stated in this work. Onthe other hand since 2D-surface accumulation series are notevidenced, one may suggest that the surface electrons havea low mobility that broadens the 2D-Landau levels and/orinhomogeneous electron concentration causing Fermi levelfluctuations that washes out the oscillations.Taking into account non-parabolicity corrections the bottomband effective mass is[m ∗ 0 = m ∗ 1 − E ]F( m∗− 1) 2 , (9)E g m 0and takes the value m ∗ 0 = 0.057 m 0. Another correction tobe taken into account is the polaron contribution. AssumingFigure 58: (a) Resistance versus magnetic field for the three samplesS1, S2 (left scale) and S3 (right scale) measured at 2 K. (b)SdH oscillations versus reciprocal magnetic field obtained fromthe magnetoresistance curves; a parabolic back-ground contributionhas been subtracted and all curves have been shifted verticallyfor clarity. (c) Temperature dependence of the oscillation amplitudefor SdH peaks with N = 3 and N = 4 Landau level index(sample S1)To summarize, electron cyclotron effective mass of InN onc-sapphire substrate is obtained from the temperature dependenceof Shubnikov-de Haas oscillations. An isotropiccyclotron effective mass equal to 0.062 ± 0.002 m 0 is measuredfor samples having bulk electron concentration in therange 1 − 4 × 10 18 cm −3 . After non-parabolicity and polaroncorrections, the effective mass at the bottom of theband is found to be m ∗ 0 = 0.055 m 0 ± 0.002.J.M. Poumirol, M. Millot, M. Goiran and J. LeotinW. Walukiewicz (Lawrence Berkeley National Laboratory, Berkeley, USA) and I. Gherasoiu (RoseStreet Labs Energy,Phoenix, USA)45