# Band Gap Vs. Lattice Constants Diagram For Hexagonal Nitride Lab Analysis

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Figure1.3: Band gap vs lattice constants diagram for hexagonal nitride compounds. The typical of measured band gap bowing for ternary alloys AlGaN and InGaN is shown by the solid line track.
1.4. Unique Material properties of Gallium Nitride:
The unique material properties of GaN engraves it as an prominent semiconductor material for many electronic and optoelectronic devices.
• The wide and direct energy band gap sorts GaN as an appropriate materials for device fabrication in the field of optoelectronics emitters (LEDs and diodes lasers) and detectors.
• Moreover the higher thermal stability along with the wide energy band gap makes GaN beneficial for high-temperature (HT) and high power electronics applications. It implies that GaN power devices reduces the high cost processing steps related with optimized complicated designed structures to
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Equations (1.4) and (1.5) can be combined to obtain the equation for piezoelectric polarization as,
P_pz=2 (a_s-a_o)/a_o (e_31-c_13/c_33 e_33) (1.6)
The total polarization P tot is calculated by summing together the two polarization components:
P_tol =〖 P〗_sp + P_pz . (1.7)
Total polarization in InGaN and AlGaN as a function of molar fraction is plotted in Fig. 1.6, assuming unstrained GaN is used as substrate. These polarization effects were found to be much stronger in c-face nitrides than in other III-V compounds. With the growth direction along the c-axis, both types of polarization add up to the surface charge density can be given by, qσ_2D=P_sp+P_pz=P_sp+2 (a_s-a_o)/a_o (e_31-c_13/c_33 e_33 ) (1.8)
Table 1.2: Calculated values for spontaneous polarization and piezoelectric constants in group III nitrides.
Paramters Materials GaN InN AlN
Spontaneous polarization, Psp (Cm−2 ) −0.034 −0.042