三五族氮化物半導體最近已引起學界與業界廣泛的研究，因為其具有相當低的介電常數及寬範圍的能帶間隙，使得發射波長涵蓋整個可見光區及部分紫外線，再加上大部分的氮化物之晶體結構為直接能隙，因此發光效率較高並且具有優異的光學特性。本文以理論計算模擬分析具wurtzite結構的氮化鋁鎵三元氮化物的結構特性及能帶性質。發現基態的Al(下標 x)Ga(下標 1-x)N三元氮化物的晶格常數以最小能量計算的結果比由Vegard's law計算的值大，其晶格常數a的偏異係數δ=-0.056±0.004 Å，晶格常數α的偏異係數δ=-0.128±0.025 Å。此外，以此晶格常數的值計算其直接能帶間隙值，發現以最小能量所得到的晶格常數所計算的結果比Vegard's law所得到的品格常數所計算的結果小。以最小能量計算的直接能帶間隙的彎曲係數b=0.957±0.026 eV，此一數值與實驗所得到的值b=1.0 eV極為接近；而以Vegard's law計算的直接能帶間隙的彎曲保數b=0.298±0.040 eV，與Kuo等人以數值模擬所得到的值b=0.353±0.024 eV亦相當吻合。
Ⅲ-nitride semiconductors have attracted both academic and technological extensive research in recent years because they have many outstanding optical properties such as lower dielectric permittivity, wide range band-gap energy from the visible region to the near ultraviolet, and direct band-gap properties that give rise to high emitting performance. This article applies numerical simulation based on ab initio to calculate the structural characteristics and the band-energy properties for wurtzite Al(subscript x)Ga(subscript 1-x) N. From this research we find that the lattice constant of the Al(subscript x)Ga(subscript 1-x) in the ground state obtained from the minimizer energy is larger than that obtained from the Vegard's law. The deviation parameter δ is -0.056±0.004 Å for lattice constant a and is -0.128±0.025 Å for lattice constant c. In addition, we also calculate the direct band-gap energy based on those lattice constants obtained by this research. We find that the direct band-gap energy obtained with the lattice constant obtained from the minimizer energy is smaller than that obtained from the Vegard's law. The bowing parameter b is 0.957±0.026 eV under the situation of the minimizer energy, which is very close to b=1.0 eV obtained from experimental data. On the other hand, the bowing parameter is 0.298±0.040 eV under the situation of applying the Vegard's law, which is also close to b=0.353±0.024 eV obtained from Kuo et al. by numerical simulation.