Light-emitting diode with a mesa constructed from a unit cell
A light-emitting device includes an n-semiconductor structure, a p-semiconductor structure and a light-emitting active-region sandwiched therebetween. An n-trough is formed to expose the n-semiconductor structure by removing a first portion of the p-semiconductor structure and the light-emitting active-region. The n-trough surrounds a p-mesa which contains a second portion of the n-semiconductor structure, the p-semiconductor structure and the light-emitting active-region. The n-trough and the p-mesa are path-connected spaces and are formed via lithography and etching using a lithographic mask which is topologically constructed via merging a unit cell's at least two transformations selected from the unit cell's translation, rotation, and reflection transformations.
1. A light-emitting device comprising an n-semiconductor structure, a p-semiconductor structure and a light-emitting active-region sandwiched therebetween;
wherein an n-trough is formed to expose the n-semiconductor structure by removing a first portion of the p-semiconductor structure and the light-emitting active-region, and the n-trough surrounds a p-mesa which contains a second portion of the n-semiconductor structure, the p-semiconductor structure and the light-emitting active-region;
wherein the n-trough and the p-mesa are path-connected spaces and are formed via lithography and etching using a lithographic mask which is topologically constructed via merging a unit cell's at least two different transformations selected from the unit cell's translation transformation, rotation transformation, and reflection transformation;
wherein the merging is a translation operation, via translating the unit cell's transformations to allow for their closest neighboring parallel portions to overlap, so as to form path-connected zero genus overlapped zones.
2. The light-emitting device according to claim 1 , wherein the unit cell is topologically a two-dimensional path-connected space with genus equal to zero.
3. The light-emitting device according to claim 1 , wherein an n-contact metal is formed on a first portion of the n-semiconductor exposed in the n-trough and a p-contact metal is formed on the p-mesa.
4. The light-emitting device according to claim 3 , wherein the n-contact metal contains an n-contact pad and the n-contact pad is used for forming electrical contact to an external power source.
5. The light-emitting device according to claim 4 , wherein the n-contact pad is located at a side of the p-mesa.
6. The light-emitting device according to claim 4 , wherein the n-contact pad is located at a center of the p-mesa.
7. The light-emitting device according to claim 5 , wherein at least one balance mesa is formed within the n-contact pad and the balance mesa is of the same height as that of the p-mesa.
8. The light-emitting device according to claim 7 , wherein the balance mesa contains the n-semiconductor structure, the p-semiconductor structure, the light-emitting active-region and the n-contact pad metal.
9. The light-emitting device according to claim 5 , wherein another mesa is provided in-between the n-contact pad and the p-mesa.
10. The light-emitting device according to claim 9 , said another mesa is a part of the p-mesa but is not path-connected to the p-mesa.
11. The light-emitting device according to claim 10 , said another mesas functions as a photodiode to reflect optical output power of the p-mesa.
12. The light-emitting device according to claim 1 , wherein the unit cell is selected from m 2 , E, E′, C 2 , G 2 , G″, G′, C, G, and n unit cells.
13. The light-emitting device according to claim 1 , wherein the unit cell is selected from the G group unit cells.