High Reflectance III-Nitride Bragg Reflectors Grown by Molecular Beam Epitaxy
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AlGaN alloy composition. A number of groups have reported the fabrication of AlGaN/GaN DBRs with peak reflectance in the near-UV to blue-green region of the spectrum [7-11]. With the employment of 30-40 quarterwave periods, peak reflectivities at 390 nm of 96% were obtained with a bandwidth of about 14 nm. DBRs based on AlN/GaN quarterwave stacks have the potential for higher peak reflectance and larger bandwidth with approximately half the number of quarterwave periods. We have previously reported that a 20.5 period DBR had peak reflectance of 95% at 392 nm [10]. The morphology and the reflectance of the structures were uniform across the 2-inch wafer. However, the simulation of the experimental data using the transmission matrix method required a variation of the thickness of the AlN (GaN) layers by as much as 30% of their nominal value. Thus in order to improve the performance of such DBRs, it is imperative to accurately control the thickness of the individual layers. Such control is more important in nitrides than in similar devices based on GaAs/AlAs because the thicknesses of the quarterwave layers in the nitrides are 400-600 Å while those for the arsenides are approximately 800-1000 Å. In this paper, we report on the growth and characterization of high reflectivity AlN/GaN DBRs with peak reflectance up to 99% and bandwidth up to 45 nm. SIMULATIONS Simulations using the transmission matrix method [12] were performed in order to design the DBR structures. The transmission matrix formulation is given by i ⋅ sin(δ r ) q B (1) cos(δ r ) 1 = nr ∏ C r =1 i ⋅ n ⋅ sin(δ ) cos(δ ) n subs r r r dr (2) δ r = 2πnr λ
dr =
λd 4 ⋅ nr
(3)
where nsubs and nr are the refractive indices of the substrate and the rth layer respectively, dr is the geometrical thickness of the corresponding quarterwave layers and λd is the target wavelength for the peak of the high reflectance band. For the simulation, we have used the thicknesses of the AlN and GaN layers of 53.1 and 46.1 nm respectively while the refractive index values of AlN, GaN (λ = 450 nm) and sapphire used were 2.12, 2.44 and 1.78 respectively. We have assumed constant refractive index values for AlN and sapphire for the wavelength region of interest (λ > 400 nm). However, the dispersion of the GaN refractive index has to be taken into account in the simulation and we have modeled it using the Sellmeir equation [13]. The optical admittance is given by
Y=
C B
(4)
and the reflectance is defined by
1 − Y 1 − Y R= 1 + Y 1 + Y
2
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(5)
Figure 1 shows the calculated peak reflectance of an AlN/GaN DBR (λ = 450 nm) with varying number of quarterwave periods. We see that a calculated peak reflectance of 99% or greater can be achieved using 16 or more periods in the DBR.
1.00
Reflectance
0.99 0.98 0.97 0.96 0.95 0.94 10
12
14
16
18
20
Number of AlN/GaN pairs Figure 1: The calculated peak reflectance of an AlN/GaN DBR (center wavelength = 450 nm) with varying number of periods from 10 to 20. EXPE
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