Study On The Structure Of Distributed Bragg Reflector And Subwavelength Grating For GaN-based VCSEL

The band gap width of the nitride material system is continuously adjustable from 0.7 e V to 6.2 e V,which makes GaN-based vertical cavity surface emitting lasers（VCSEL）cover the ultraviolet to visible region,just complementary to the already mature Ga As-based VCSEL covering the infrared band.Therefore,GaN-based VCSEL has attracted extensive attention of researchers.As an important part of GaN-based VCSEL,reflectors with high reflectivity and wide stopband can reduce the threshold current and increase the laser output power of VCSEL.Based on the theoretical analysis,distributed Bragg reflectors（DBR）and subwavelength grating（SWG）are designed for the green（λ₀=0.52μm）GaN-based VCSEL,providing theoretical guidance for the structural design of GaN-based VCSEL reflectors.The main research contents are as follows:（1）As a traditional reflector of VCSEL,DBR is composed of two materials with large refractive index difference grown alternately withλ₀/（4n）thickness.This paper studies nitride DBR:Al N/GaN DBR and Al Ga In N/In GaN DBR.The reflectance spectrum of Al N/GaN DBR is calculated by using the transfer matrix method combined with the refractive index dispersion model.It is found that under the same conditions,the high-refractive-index material as the first layer（HL structure）of DBR has higher reflectivity and wider stopband than the low-refractive-index material as the first layer（LH structure）.According to the simulation calculation,the growth of a layer of high-refractive-index material on the integer pairs DBR（A pair of DBR refers to a layer of high and low refractive index materials）does not affect the reflection spectrum performance.Due to the large refractive index difference between Al N and GaN materials,Al N/GaN DBR can achieve high reflectivity and wide stopband with relatively few pairs.However,the large lattice mismatch between the two materials will lead to cracks and dislocations when there are too many growth pairs.Therefore,Al Ga In N/In GaN DBR of strain compensation is further studied.In order to increase the refractive index difference between Al Ga In N and In GaN,Al Ga In N material with high Al component（Al component 0.8）is selected.According to the strain compensation principle,the overall strain of DBR is required to be 0.The strain-compensated Al Ga In N and In GaN material components can be calculated,and their reflection spectra can be calculated using the transfer matrix method.It is shown that the reflectance of 30 pairs of Al_0.8Ga_0.18In_0.02/In_0.172Ga_0.828N DBR exceeds 99.5%at the central wavelength and the stopband width reaches 26 nm.With the increase of In content in Al Ga In N material,reflectivity and stopband width decrease.For Al N/GaN DBR and Al Ga In N/In GaN DBR,both reflectivity and stopband width increase with the increase of DBR pairs.However,when the pairs reaches a certain number,increasing DBR pairs will not have much influence on reflectivity and stopband,but will affect the quality of DBR in the actual production process.（2）SWG can replace DBR as the top reflector of VCSEL,which is a periodic grating structure formed by two kinds of high and low refractive index materials.High reflectivity and wide stopband can be obtained by adjusting the grating structure parameters.The effects of different grating parameters on the diffraction efficiency of SWG are simulated by using the rigorous coupled-wave analysis,and the diffraction anomalies under transverse electric wave（TE polarization）and transverse magnetic wave（TM polarization）are studied.In this paper,we focus on one-dimensional Ti O₂ SWG,Si₃N₄ SWG and GaN SWG.The simulation results show that Rayleigh anomaly and leakage mode resonance effect occur in both TM and TE polarization states.TE polarization produces a broad flat band covering the central wavelength,while the reflection spectrum peak of TM polarization is sharper and does not coincide with the TE polarization peak.In order to achieve high reflectivity at the central wavelength,the effect of each parameter on diffraction efficiency under TE polarization is mainly studied.It is found that the optimal grating period,height and duty cycle for Ti O₂ SWG are 0.49μm,0.25μm and0.34,respectively,with fabrication tolerances of 1.6%,2.0%and 8.3%for each parameter.Considering the trapezoidal grating structure in the actual manufacturing process,the difference between the top and bottom duty cycleΔf₀ should be controlled at-10%～5%.The optimal grating period,height and duty cycle of Si₃N₄ SWG are 0.489μm,0.2μm and 0.5,respectively,and the fabrication tolerance of each parameter is 1.6%,3.0%and 1.4%.The difference between the top and bottom duty cycleΔf₀ should be controlled at-1%～3%.The optimal grating period,height and duty cycle of GaN SWG are 0.475μm,0.17μm and 0.52,respectively,and the fabrication tolerances of each parameter are 3.1%,15.8%and 1.9%.The difference between the top and bottom duty cycleΔf₀ should be controlled at-1%～2%.The optimal parameters of one-dimensional Ti O₂ SWG,Si₃N₄ SWG and GaN SWG all have reflectance over 99.9%at the central wavelength of 0.52μm,and the width of the high reflectance band（reflectance greater than 99.9%）reaches 26 nm,35 nm and 62 nm,respectively,which can all be used as reflectors for GaN-based VCSEL based on the theoretical analysis.