Nitride based semiconductor light-emitting device

1. A semiconductor device having a semiconductor multi-layer structure which includes at least one active layer including at least one luminescent layer of In x Al y Ga 1−x−y N (0<x<1, 0≦y≦0.2), and at least a part of said at least one luminescent layer acting as a quantum well,

wherein said semiconductor device satisfies at least one of:

a first condition that a threshold mode gain of said quantum well is more than 12 cm −1, and

a second condition that said semiconductor device has an internal loss “α i ” (cm −1 ) which satisfies α i >12xn −α m (cm −1 ), where “α m ” is a mirror loss, and “n” is a number of said quantum well; and

a third condition that said semiconductor device has a slope efficiency “S” (W/A) which satisfies: S<3×{α m /(12×n)}×[{(1−R 1 )√(R 2 )}/{(1−√(R 1 R 2 ))×(√(R 1 )+√(R 2 ))}], where “R 1 ” is a first reflectance of a first cavity facet, from which a light is emitted, “R 2 ” is a second reflectance of a second cavity facet opposite to said first cavity facet, “α m ” is a mirror loss, and “n” is a number of said quantum well, and

wherein a differential gain “dg/dn” of said at least one active layer satisfies dg/dn≧1.0×10 −20 (m 2 )1 and

standard deviations of microscopic and macroscopic fluctuations in a band gap energy of said at least luminescent layer are not more than 40 meV; and

wherein said microscopic fluctuation is measured based on temperature dependence of a photoluminescence lifetime and wherein said microscopic fluctuation is controlled by heat treatment of said semiconductor device at a temperature between 850° C. and 1200° C.

2. The semiconductor device as claimed in claim 1 , wherein said semiconductor device has a cavity length “L” of not less than 1000 micrometers, and said first reflectance “R 1 ” is not more than 20%, said second reflectance “R 2 ” is not less than 80% and less than 100%, and said slope efficiency “S” satisfies S<2.1/n (W/A).

3. The semiconductor device as claimed in claim 1 , wherein said semiconductor multi-layer structure comprises a gallium-nitride-based multi-layer structure.

4. The semiconductor device as claimed in claim 3 , wherein said gallium-nitride-based multi-layer structure extends over a gallium-nitride-based substrate.

5. The semiconductor device as claimed in claim 3 , wherein said gallium-nitride-based multi-layer structure extends over a sapphire substrate.

6. The semiconductor device as claimed in claim 3 , wherein said gallium-nitride-based multi-layer structure extends over a substrate having a surface dislocation density of less than 1×10 8 /cm 2 .

7. The semiconductor device as claimed in claim 1 , wherein a standard deviation “Δ x ” in the “microscopic fluctuation” of the indium composition is not more than 0.067.

8. The semiconductor device as claimed in claim 7 ,

wherein said semiconductor device has a slope efficiency “S” (W/A) which satisfies:

S< 3×{α m /(12 ×n )}×[{(1 −R 1 )√( R 2 )}/{(1−√( R 1 R 2 ))×(√( R 1 )+√( R 2 ))}],

where “R 1 ” is a first reflectance of a first cavity facet, from which a light is emitted, “R 2 ” is a second reflectance of a second cavity facet opposite to said first cavity facet, “α m ” is a mirror loss, and “n” is a number of said quantum well.

9. The semiconductor device as claimed in claim 8 , wherein said semiconductor device has a cavity length “L” of not less than 1000 micrometers, and said first reflectance “R 1 ” is not more than 20%, said second reflectance “R 2 ” is not less than 80% and less than 100%, and said slope efficiency “S” satisfies S<2.1/n (W/A).

10. The semiconductor device as claimed in claim 7 , wherein said semiconductor device has an internal loss “α i ” (cm −1 ) which satisfies α i >12×n−α m (cm −1 ), where “α m ” is a mirror loss, and “n” is a number of said quantum well.

11. The semiconductor device as claimed in claim 7 , wherein said semiconductor device has a photo-luminescence peak wavelength distribution of not more than 40 meV in said active layer.

12. The semiconductor device as claimed in claim 1 , wherein the microscopic fluctuations are not more than 20 meV.

13. The semiconductor device as claimed in claim 1 , wherein a dispersion degree of a thermal carrier in said active layer is estimated by varying a temperature measurement, so as to determine said microscopic fluctuation.