A feedback modification method based on variable separation mapping is proposed in the design of free-form optical system with uniform illuminance for LED source. In this method, the non-negligible size of LED source is taken into account, and a smooth optical system is established with single freeform surface regenerated by adding feedback to the lens design for a point light source. More rounds of feedback can improve the lens performance. As an example, a smooth free-form lens with rectangular illuminance distribution is designed, and the illuminance uniformity is improved from 18.75% to 81.08% after eight times feedback.
For the problem of point source forming prescribed irradiance, a new, to the best of our knowledge, method-variable separation mapping method is presented, which establishes separately the correspondence between variables on the light source and the target plane. The role played by the optical surfaces is then to redirect the light rays to their corresponding target points. The surface of the lens is determined by first calculating the surface points and then their normal vectors. Considering that normal deviations are produced in the surface construction process, a normal deviation control method is also presented to restrict the deviation. With this normal deviation control method, discontinuities are introduced onto the lens surface. From these mapping and normal control methods, a fast and efficient algorithm has been developed for several prescribed irradiance problems with simple nonrotational shape of the illuminated region.
to 6.2 eV for AlN, [3] which spans the entire ultraviolet and visible band [4][5][6][7] as well as the near-infrared region. [8,9] Accordingly, III-nitrides have been widely adopted for the fabrication of light-emitting diodes (LEDs), [10][11][12] laser diodes (LDs), [13][14][15] photodetectors (PDs), [16][17][18] and solar cells. [19][20][21] Furthermore, the spontaneous and piezoelectric polarization in wurtzite semiconductors [22][23][24][25] and the high electron drift velocities [26][27][28] can be used to fabricate high electron mobility transistors based on two-dimensional (2D) electron gas (2DEG) in AlGaN/GaN heterostructures. [29][30][31][32] At present, by employing metal organic chemical vapor deposition (MOCVD), [3,[33][34][35] molecular beam epitaxy (MBE), [36][37][38][39] or hydride vapor phase epitaxy (HVPE), [40][41][42] III-nitride films with high crystalline quality can be obtained on c-plane sapphire, [43][44][45] Si (111), [38,[46][47][48] or 6H-SiC [49][50][51] substrates at a high growth temperature, usually above 1000 °C. [52][53][54] However, exfoliating III-nitride films from such single-crystalline substrates proves difficult because of the strong sp 3 -type covalent bonds between the substrates and epilayers. [55] To overcome this problem, thermal release through laser radiation, [56,57] stamp-based printing, [58,59] chemical etching, [60][61][62][63][64][65][66][67] and mechanical exfoliation [54,55,68,69] from singlecrystalline substrates have been investigated. However, there still remain some bottlenecks for future applications, such as damage, limited size, and tedious steps of the flexible production process. [55] Furthermore, flexible amorphous substrates generally cannot tolerate such high growth temperature, [54] and cannot be used for epitaxial growth of single-crystalline films because of the unordered surface atomic arrangement. [70,71] Hence, it is extremely difficult to make allowance for wearable and foldable applications of next-generation (opto)electronic devices based on III-nitrides. [72] On the other hand, sp 2 -bonded 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) exhibit hexagonal in-plane lattice arrangements and weakly bonded layers. [54,73,74] If sp 3 -bonded III-nitride films can somehow be grown on sp 2 -bonded 2D materials, it is theoretically possible to transfer these functional films onto foreign flexible substrates because of the weak van der Waals interactions on both sides of the 2D materials. [68,75,76] In this case, the 2D materials not only act as a buffer layer but also provide a release layer for the mechanical exfoliation of solid-state lighting, flat-panel displays, and solar energy and power electronics. Generally, GaN-based devices are heteroepitaxially grown on c-plane sapphire, Si (111), or 6H-SiC substrates. However, it is very difficult to release the GaN-based films from such single-crystalline substrates and transfer them onto other foreign substrates. Consequently, it is difficult to meet t...
Two light-emitting diode samples are grown with InGaN and GaN underlying layers beneath the multiple quantum wells (MQWs), respectively. By measuring the carrier lifetime as a function of photon energy, it is found that the MQW with InGaN underlying layer has a higher degree of carrier localization. Comparison between the external quantum efficiency and injection current of these two samples reveals that efficiency droop at small injection current is attributed to the delocalization of carriers, while further droop at a higher injection current is due mostly to the carrier leakage demonstrated through temperature-dependent electroluminescence measurements.
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