Determination of effective mass in InN by high-field oscillatory magnetoabsorption spectroscopy

We report on oscillatory magnetoabsorption experiments on several indium nitride (InN) epilayers under a pulsed magnetic field up to 56 T. This optical technique is uniquely suited to probe the bulk electronic structure in the vicinity of the fundamental band edge by Landau level spectroscopy. We discuss these results in light of two recent studies on the InN band structure by high-field magnetotransport [Goiran et al., Appl. Phys. Lett. 96, 052117 (2010)] and magneto-photoluminescence [Pettinari et al., Phys. Rev. B 79, 165207 (2009)]. In particular, we evidence a strong nonparabolicity of the conduction band and demonstrate that the electron effective mass $m_{e\perp 0}^{*}=0.055m_0$ measured by Shubnikov–de Haas oscillations is confirmed by the magneto-optical experiments.

Figure 1

Contour plot of the transmitted light intensity divided by the zero-field intensity as a function of the applied magnetic field up to $56$ T. Black corresponds to a high transmission. Left inset: Investigated samples side view with a 1 $\mu$m InN epilayer on a thin GaN buffer layer. Right inset: Schematic view of the present oscillatory magnetoabsorption experiments: under a strong magnetic field a photon can be preferentially absorbed if its energy matches the energy gap between an orbiting hole and an orbiting electron belonging to Landau levels with the same quantum number $N$.

Figure 2

Normalized spectra of transmitted light through the InN crystal B at selected values of the applied magnetic field up to $56$ T. Arrows indicate the OMA bands. Inset: Room temperature band-edge absorption spectrum of sample D recorded at zero field. The extrapolated value of the band gap (arrow) and the cut-off energy (dotted line) of the spectrometer used to record the OMA spectra are indicated.

Figure 3

(a) OMA fan chart of the three InN samples, measured at 77 K. The nonaccessible energy range appears in light grey. (b) OMA band energies as a function of the renormalized magnetic field $\mathrm{B̃}=(N+1/2)\hslash eB/m_0$ for sample B. The circles have been disregarded for the fit procedure.[23] Linear best fit is shown as a black dotted line. Nonlinear best fit is based on Eq. (7) with the electron effective mass value at the bottom of the band $m_{e\perp 0}^{*}=0.055m_0$ (solid blue line). Left inset: Residual of the linear fit. Right inset: Residual of the nonlinear fit. (c) Measured OMA energies for sample B and calculated values using the results of the linear (black dotted line) and nonlinear (solid blue line) fits.