Study On The Calculation Of GaN Bandgap And The Change With Temperature

The rise of the third generation of wide bandgap semiconductors has promoted the tremendous advancement of semiconductor technology and the prosperity of the semiconductor optoelectronic device industry.Compared with the previous two generations of semiconductors,the third-generation semiconductors have a forbidden band width spanning 0.7eV-6.2eV,covering the entire visible light band,and thus are widely used in solid-state lighting.In recent years,semiconductor optoelectronic devices have often operated over a relatively large temperature range,which requires us to understand the physical mechanism of the band structure of semiconductor materials as a function of temperature.In addition,different types of doping are effective means to improve the photoelectric properties of semiconductors and enhance the performance of photovoltaic devices.It is necessary to understand the effects of different concentrations of different elements on the properties of the semiconductor Taking GaN as an example,this paper will use the first principle to calculate the energy band structure,density of states and optical properties of intrinsic GaN and GaN with different concentrations of n-type doping(Si doping)and p-type doping(Mg doping),which will theoretically support the subsequent spectral studies of intrinsic,p-doped and n-doped GaN samples.In this paper,two kinds of wurtzite GaN(u-type and n-type)samples were prepared for temperature-dependent PL study,and the relationship between the forbidden band width and temperature of high-quality undoped GaN samples was investigated.The following conclusions were obtained:1.Local Density Approximation(LDA)exchange correlation function and norm-conserving pseudopotential have the best effect on the first-principle geometry optimization of intrinsic GaN.The3d,4s and 4p orbitals of Ga and the 2s and 2p orbitals of N contribute to the density of states.Among them,the density of states of the valence band is mainly composed of the contribution of N's 2p orbital and a little Ga's 4p orbital.The refractive index of GaN reaches the maximum and minimum values at the photon energies of 5.07 eV and 16.35 eV,respectively,and the extinction coefficient reaches a maximum at 11.75 eV;its reflection coefficient and absorption coefficient reach a maximum at 13.65 eV and 13.15 eV,respectively.2.1)The lattice constants a and c of Si-doped GaN decrease with increasing doping concentration.The 3s and 3p orbitals of Si contribute to the density of states.As the concentration increases,the 3s and 3p orbital will contribute to the density of states of the conduction band towards the higher energy which will broaden the band.And the density of states contributed by the3p orbital below the bottom of the conduction band will introduce the donor level.2)The lattice constants a and c of Mg-doped GaN increase as the doping concentration increases.The 3s and 2p orbitals of Mg contribute to the density of states.As the concentration increases,Mg's 2p orbital will gradually contribute more to the introduction of the acceptor level.3.The Varshni model ignores the phonon mechanism and does not agree with the real physics.The model underestimates the dependence of the GaN bandgap on temperature in the low temperature region and exhibits a big systematic bias.With the increase of temperature,the model will be more and more deviated from the actual temperature dependence of GaN bandgap,showing more and more errors.2)The theoretical starting point of the Bose-Einstein model has a certain physical basis,but the simple mathematical form of the model has a strong judgment on the temperature dependence of the GaN band gap in the low temperature region which shows a tendency of the system to be small.In the temperature range studied,the model is unstable to the GaN bandgap temperature dependence and exhibits systematic changes with repeated changes.4.The model based on the physics mechanism of energy band contraction can flexibly use the electron-phonon spectral function f(e)to describe the relationships between electrons and phonons in GaN.The linear function and the power function of the electron phonon spectral function are not realistic for the GaN state density,so the energy of the main phonon which linear model and the power model infer that affects the temperature dependence of GaN bandgap goes beyond the phonon spectral energy range of Ga N.The ? model has a good mathematical approximation of the temperature dependence of the GaN bandgap,but because its mathematical approximation of the GaN state density is too simple to completely believe the conclusion that acoustic phonon in GaN mainly affects the temperature dependence of bandgap.5.The combined model and the two-phonon model(multi-phonon model)consider the distribution characteristics of phonon spectral in GaN and make a complex practical detailed mathematical approximation for the GaN state density.The judgment of which phonon mainly affects the temperature dependence of the band gap temperature dependence and Mathematical estimation of band gap with temperature is the most accurate.We can see that the optical phonons in intrinsic GaN make a major contribution to the temperature dependence of the band gap.