By making use of the density functional theory (DFT) of the first principles and generalized gradient approximation method , the electronic structures and properties of ideal GaN and AlxGa1-xN crystals (x = 0.25, 0.5, 0.75) have been calculated and analyzed, and the influence of the doping quantity of x on the characteristics of AlxGa1-xN has been studied. The calculation results show that optical band gap of AlxGa1-xN crystal is widened that the Eg of AlxGa1-xN can be adjusted by the x, and the absorption spectrum shifts to high-energy direction with the increase of the x, and then the Fermi energy moves to the top of valence band slightly which leads to that conductivity weakened after mixed with the Al. At the same time, the variation trends of complex dielectric function, absorption spectrum and transitivity have been made clear, and the results show that AlxGa1-xN compounds can achieve the theoretical design of photoelectric performance. In a word, AlxGa1-xN crystals are potential semiconductors with very remarkable photoelectric properties, which can be applied in the development of the diversified GaN devices.
With the development of microelectronic technology, the GaN-based semiconductors, which have wide band gap, high breakdown voltage, high thermal conductivity and good physical and chemical stability [
The crystal structure of the GaN model adopted in this paper is hexagonal wurtzite structure, which belongs to P63mc space group and symmetry, and the lattice constant is a = b = 0.3189 nm, c = 0.5185 nm, α = β = 90˚, γ = 120˚ [
of Al are 25%, 50%, 75%, 100%, respectively.
The calculation use the CASTEP module of MS5.0 software based on the DFT’s ab initio quantum mechanics, which adopts plane wave pseudopotential method and the exchange-correlation energy employs the PW-91 approximation method under the generalized gradient approximation (GGA). In order to ensure the convergence of system energy in the level of quasi perfect plane fundamental wave under the permission situation of the hardware resources, K grid is selected as 4 × 4 × 2 and the cutoff energy of the plane wave is 310 eV, and a single-atom convergence precision is 2.0 × 10−5 eV/atom, and then the internal stress is not more than 0.1 GPa [
The band structure of 2 × 2 × 2 GaN super-cell model can be calculated, which is shown in
The calculated electron density of states of GaN is given in
Considering the relationship between the absorption
coefficient and the complex refractive index [
In the formula, K is the wave vector of electron, C and V are the valence band and conduction band, BZ is the first Brillouin zone, Ψ is the wave function, û is electric vector, and are the intrinsic energy levels on conduction band and valence band.
By calculating 2 × 2 × 2 intrinsic GaN super-cell model in
to ones of the complex dielectric function, but the difference of the peak strength are relative large. The strongest peak of the absorption spectrum situates at 9.5 eV approximately, which is from the transitions of 3d state electron of Ga and 2p state electron of N in
By using the equations above, the transmittance (α is the absorption coefficient, is the normalized reflection coefficient R) can be deduced and calculated, as shown in
A series of band structures of AlxGa1−xN crystal models mixed with different Al component of 25%, 50%, 75%, and 100% are calculated respectively, and the band-gap widths are listed in
software, the band gap values of the theoretical calculation, namely “Origin values” are very low, and the Test values are the ones modified by adding the scissor difference.
The curve of density of states of Al0.5Ga0.5N crystal is computed as
The imaginary part of dielectric function of Al0.5Ga0.5N is calculated and shown in
peaks are degenerated by 5 peaks of GaN while the peak positions of Al0.5Ga0.5N move slightly to high energy region, and the main peak is located at 8 eV whose peak value did not change basically, which is resulted from that the optical band gap become wide after the Al doped and shows the electronic transitions of Al0.5Ga0.5N is more different than GaN. As can be seen from the above curves, the dielectric peak values slightly increase and the peak position keeps moving to the high energy region with the amount increasing of Al doping.