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Optical polarization properties of m-plane Al x Ga1- x N epitaxial films grown on m-plane freestanding GaN substrates toward nonpolar ultraviolet LEDs

Kouji Hazu and Shigefusa F. Chichibu

Open Access Open Access

Abstract

Light polarization characteristics of the near-band-edge optical transitions in m-plane AlxGa1- xN epilayers suffering from anisotropic stresses are quantitatively explained. The epilayers were grown on an m-plane freestanding GaN substrate by both ammonia-source molecular beam epitaxy and metalorganic vapor phase epitaxy methods. The light polarization direction altered from E⊥c to E//c at the AlN mole fraction, x, between 0.25 and 0.32, where E is the electric field component of the light and ⊥ and // represent perpendicular and parallel, respectively. To give a quantitative explanation for the result, energies and oscillator strengths of the exciton transitions involving three separate valence bands are calculated as functions of strains using the Bir-Pikus Hamiltonian. The calculation predicts that the lowest energy transition (E 1) is polarized to the m-axis normal to the surface (X 3) for 0<x≤1, meaning that E 1 emission is principally undetectable from the surface normal for any in-plane tensile strained AlxGa1- xN. The polarization direction of observable surface emission is predicted to alter from c-axis normal (X 1) to c-axis parallel (X 2) for the middle energy transition (E 2) and X 2 to X 1 for the highest energy transition (E 3) between x = 0.25 and 0.32. The experimental results are consistently reproduced by the calculation.

©2011 Optical Society of America

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Figures (10)
Fig. 1
Fig. 1 (a) Schematic drawing of a c-plane FS-GaN boule grown on a c-plane Al2O3 substrate by HVPE and a sliced m-plane FS-GaN. (b) X-ray rocking curves for the (100) diffraction of the m-plane FS-GaN. The x-rays were irradiated along the c-axis or a-axis, as shown in panel (c). (d) Schematic diagram of the notations of three axes.

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Fig. 2
Fig. 2 Representative X-RSM images for the pseudomorhic m-plane Al0.25Ga0.75N epilayer grown on the m-plane FS-GaN taken in the vicinity of (a) (130) and (b) (201) diffraction spots. The X-RSM images for partially lattice-relaxed Al0.70Ga0.30N epilayers taken for (c) (120) and (d) (201) diffractions. Both the epilayers were grown by NH3-MBE. The closed circle in each panel shows the location of strain-free AlN, for comparison.

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Fig. 3
Fig. 3 (a) FWHM values for the XRCs (Δω mc , Δω ma , and Δω r ) of m-plane Al x Ga1- x N epilayers grown by NH3-MBE and MOVPE. (b) Strain components ε X 1 X 1 , ε X 2 X 2 , and ε X 3 X 3 of the m-plane Al x Ga1- x N films as a function of AlN mole fraction x.

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Fig. 4
Fig. 4 (a) Polarized CL spectra at 12 K of m-plane Al x Ga1- x N epilayers grown on the m-plane FS-GaN substrates. (b) Polarization ratios, which are defined as ( I X 1 − I X 2 ) / ( I X 1 + I X 2 ) , of the Al x Ga1- x N films as a function of AlN mole fraction x. Corresponding values calculated using the relative oscillator strengths are also shown. The films of x≤0.70 were grown by NH3-MBE and x≥0.73 were grown by MOVPE.

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Fig. 5
Fig. 5 Relative oscillator strengths of E 1, E 2, and E 3 transitions for the m-plane GaN film as functions of in-plane strain coordinate ( ε X 1 X 1 , ε X 2 X 2 )   . Closed circles indicate the experimentally obtained in-plane strain coordinate ( ε X 1 X 1 , ε X 2 X 2 ) = ( 0.00 % , 0.00 % ) , which are plotted on the respective predominant polarization directions.

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Fig. 6
Fig. 6 Relative oscillator strengths of E 1, E 2, and E 3 transitions for the m-plane Al0.03Ga0.97N film as functions of in-plane strain coordinate ( ε X 1 X 1 , ε X 2 X 2 )   . Closed circles indicate the experimentally obtained in-plane strain coordinate ( ε X 1 X 1 , ε X 2 X 2 ) = ( 0.08 % , 0.13 % ) , which are plotted on the respective predominant polarization directions.

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Fig. 7
Fig. 7 Relative oscillator strengths of E 1, E 2, and E 3 transitions for the m-plane Al0.70Ga0.30N film as functions of in-plane strain coordinate ( ε X 1 X 1 , ε X 2 X 2 )   .   Closed circles indicate the experimentally obtained in-plane strain coordinate ( ε X 1 X 1 , ε X 2 X 2 ) = ( 0.79 % , 0.35 % ) , which are plotted on the respective predominant polarization directions.

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Fig. 8
Fig. 8 Relative oscillator strengths of E 1, E 2, and E 3 transitions for the m-plane Al.N film as functions of in-plane strain coordinate ( ε X 1 X 1 , ε X 2 X 2 )   . Closed circles indicate the experimentally obtained in-plane strain coordinate ( ε X 1 X 1 , ε X 2 X 2 ) = ( 0.25 % , 1.96 % )   . They are plotted on the outside of the frameworks of respective predominant polarization directions.

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Fig. 9
Fig. 9 Calculated E 1, E 2, and E 3 exciton transition energies for the m-plane (a) GaN, (b) Al0.03Ga0.97N, (c) Al0.70Ga0.30N, and (d) AlN films. The energy difference between E 2 and E 1, (E 2-E 1), as functions of in-plane strains ( ε X 1 X 1 , ε X 2 X 2 ) for the m-plane (e) GaN, (f) Al0.03Ga0.97N, (g) Al0.70Ga0.30N, and (h) AlN films. Closed circles indicate respective in-plane strains.

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Fig. 10
Fig. 10 Calculated E 2 transition energies (closed squares), measured CL peak energies (open circles), and their energy differences (closed diamonds) for the m-plane Al x Ga1- x N films as a function of x.

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Tables (2)

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Table 1 Optical Constants of Thin Films of Materials a

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Table 2 Calculated polarization directions for E 1, E 2, and E 3 transitions and energy differences between E 1 and E 2 band (E 2-E 1).

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Equations (1)

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ε + = ε x x − ε y y + 2 i ε x y .
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