Physics homework help
Crystal Structure/Band Structure (Physics)
Numerical simulation
Final report: Comparisonsimulation data of Si4N3 dielectric material
(doi:10.17188/1197656)
- Introduction
Silicon nitride (Si3N4) is a non-metallic compound composed of silicon and nitrogen.This material is interesting because of its durability, electrical insulation, high thermal stability and high acid resistance that widely used in microelectronics and micro-surface machining technologies. Physics homework help
The micro-bolometer devices were fabricated at nano and energy center (NEC) of Vietnam national university (VNU) used Si3N4 shut as a supporting layer for the suspending structure and in absorption infrared radiation (IR) packet. The fabrication method used plasma enhanced chemical vapour deposition (PECVD) system that require high vacuum. The optimization of IR absorption packet by experimental is extremely expensive. Thus, the properties of Si3N4 crystal structure need to investigate by simulation and compare to experiment data. Physics homework help
ORDER A PLAGIARISM-FREE PAPER NOW
- Simulation data
Structure
| Space group | P 1 | |
|
Direction |
a | 7.80919 Å |
| b | 7.80919 Å | |
| c | 5.65995 Å | |
| V | 298.9199 Å3 | |
| α | 90 o | |
| β | 90 o | |
| γ | 120 o | |
Figure 1: The crystal structure of Si3N4 trigonal
Space group:
| Hermann Mauguin | P31c |
Hall |
P 3 c |
Point Group |
3m |
Crystal System |
trigonal |
Figure 2: Space group P31c
| Symmetry operators | |
| 1 | 1 |
| 2 | 3+ (0, 0, z) |
| 3 | 3– (0, 0, z) |
| 4 | c (x, x, z) [0, 0, |
| 5 | c (x, 0, z) [0, 0, |
| 6 | c (0, y, z) [0, 0, |
Table 2: Symmetry Operators of Space group P31c
Band gap
Density functional theory is formulated to calculate ground state properties. Although the band structure involves excitations of electrons to unoccupied states, the Kohn-Sham energies used in solving the density functional theory (DFT) equations are often interpreted to correspond to electron energy levels in the solid.The correspondence between the eigenvalues of the Kohm-Sham calculated by the DFT and the real electron energy is theoretically only theoretically valid for the highest occupied electron state. The Kohn-Sham energy of this state matches the first ionizing energy of the material, giving an exact exchange correlation function. For other energies, however, there is no guarantee that the specific values of Kohn-Sham will correspond to observable objects. Physics homework help
According to Kohn- Sham the density functional theory (DFT) was wrote:
Where E(r) is the function of electron density r(r) that called exchange -correlation function. The electron density can calculated by equation below:
Finally, the Hamiltonian was presented by:
And the particle m can be shonw by the mthsolution of equation
However, we still don’t know the last term xc(r) leading to the development of approximation methods. Some typical approximations are Thomas – Fermi, Hartree – Fock, Kohn – Sham…
Figure 3: The band structure of Si3N4 crystal structure
Figure 3 shows that the indirect bandgap value in this case is K -G = 4.658 eV. Physics homework help
XRD spectra
Figure 4: XRD spectra -αCu flowing the simulation data from material project of Si3N4 mp-2245 and the data take from databased from crystallography open database.
As shows in figure 4, The peak of simulation data is the same with open experiment data. However, the Intensity of the databased peak is different depend on the measurement system and the defect in the sample.
Reference data:
COD ID:1001238: Materials Research Bulletin, 1983, 18, 921-934
COD ID:1001239: Materials Research Bulletin, 1983, 18, 921-934
COD ID:1001240:Materials Research Bulletin, 1983, 18, 921-934
COD ID:1001241:Materials Research Bulletin, 1983, 18, 921-934
COD ID:1001242:Materials Research Bulletin, 1983, 18, 921-934
COD ID:1001243:Materials Research Bulletin, 1983, 18, 921-934. Physics homework help
