Semiconductor light emitting element and method for producing the same
A semiconductor light emitting element with a design wavelength of λ, comprising a photonic crystal periodic structure having two structures with different refractive indices at each of one or more interfaces between layers that form the light emitting element. The period a and the radius R that are parameters of each of the one or more periodic structures and the design wavelength λ satisfy Bragg conditions. The ratio (R/a) between the period a and the radius R is a value determined so that a predetermined photonic band gap (PBG) for TE light becomes maximum for each periodic structure. The parameters of each periodic structure are determined so that light extraction efficiency of the entire semiconductor light emitting element with respect to light with the wavelength λ becomes maximum as a result of conducting a simulation analysis with a FDTD method using as variables the depth h of the periodic structure that is of greater than or equal to 0.5a and the period a and the radius R that are determined for each order m of the Bragg conditions.
1. A semiconductor light emitting element with a design wavelength of λ, comprising:
a transmitted-type photonic crystal periodic structure including a plurality of pillar structures, each having a radius of R at a backside of a substrate, wherein the photonic crystal periodic structure is formed by two-types of structures, air having a refractive index n 2 , and the substrate having refractive index n 1 ,
wherein the photonic crystal periodic structure has two photonic band gaps, wherein the photonic band gaps are open for TM polarization component, and have an average refractive index n av of the two-types of structures, the average refractive index n av satisfies Bragg conditions mλ/n av =2a, wherein n av is calculated by the equation of n av =(n 2 2 +(n 1 2 −n 2 2 )(2π/√3)(R/a) 2 ) 1/2 , a is a period of the pillar structures, an order m of the Bragg conditions is 4, 0.31≤R/a≤0.36, and a depth of each of the pillar structures h≥0.5a.