侧墙倾斜的水平半导体/空气分布布喇格反射器的设计

Design for Horizontal Semiconductor-Air Distributed Bragg Reflectors with the Tilt of Vertical Sidewall

时域有限差分(FDTD)法计算表明,在常规的水平半导体/空气分布布喇格反射器(DBR)设计中为了得到高反射率,DBR中侧墙与衬底垂直非常重要。对于GaN基材料DBR侧墙如果有3°的倾斜,反射率将下降到30%左右,然而在实验上很难得到侧墙与衬底垂直的GaN基DBR结构。考虑到侧墙倾斜问题我们提出了新的DBR设计方法,采用这种方法即使DBR侧墙有较大的倾斜也可以得到高的反射率。设计的关键是在侧墙倾斜的情况下保持每个DBR周期光程差与垂直情况下一致,根据光的干涉原理我们给出了详细的解释。

It has been shown that high reflectivity mirrors can be formed by deeply etched semiconductor/air distributed Bragg reflectors （DBRs）. The DBR structures are almost identical to multilayers of semiconductor and air. Current etching technologies can produce deep uniform etches in semiconductors. The finite difference time domain （FDTD） method directly solves Maxwell＇s equation in time. It is remarkably robust, providing accurate modeling for various electromagnetic wave interaction and field problem. Rapid advances in computer technology make the FDTD method more and more attractive every day. In this work we use the FDTD method in two dimensions to study a GaN-based semiconductor/air DBR structure. We take account of the TE mode and considering the geometry to be invariant in the lateral direction perpendicular to the light propagation. The spectral reflectivity is calculated by comparing the spectral content of the incident and reflected pulse. FDTD simulations show that vertical sidewall tilt is a crucial concern for obtaining a high-reflectivity DBR in a conventional design. The middle widths of semiconductor should increase to obtain the high reflectivity with the sidewall angle decreasing. To obtain high reflectivity at designed wavelength, the difference of optical path for one DBR pitch should keep constant. When the sidewall tilted, the difference of optical paths decrease. This phenomena can be explained using the knowledge of interference. To increase the optical paths difference, the air space and/or semiconductor width should be increased. The increase of air space will also increase the diffractive spreading loss, which arises because modal confinement is limited to the semiconductor region. In the air gaps, light is not confined and the refractive index of the air is much lower than that of the semiconductor, the optical field diverges quickly upon reaching the semiconductor-air interface. So, the semiconductor width should be increased to increase the optical width. Thus, high reflectivity can be reached with the proper design even with a large vertical sidewall tilt. Experimentally, it is difficult to etch vertical sidewalls of GaN-based materials, so the new design to overcome this difficulty is very meaningful.