Table 4 Material parameters used for mole fraction x = 0.2 in our Monte Carlo simulation.

Parameters	GaN	AlN	InN	Al_0.2Ga_0.8N	In_0.2Ga_0.8N	In_0.2Al_0.8N
M (kg/m³)	6087	3230	6240	5515.6	6117.6	3832
v_s (m/s)	7619	9060	3780	7907	6851.2	8004
D_a (eV)	8.3	6.2	4.76	7.88	7.05	5.37
\({\varepsilon }_{s}\)	9.7	8.5	15.3	9.46	10.82	9.86
\({\varepsilon }_{\infty }\)	5.28	4.77	8.4	5.18	5.904	5.496
\({m}_{\Gamma }\)	0.2	0.48	0.04	0.256	0.168	0.392
\({m}_{\mathrm{U}}\)	0.4	1	0.25	0.52	0.53	0.85
\({\mathrm{m}}_{{\Gamma }_{3}}\)	0.6	1	1	0.68	0.52	1
\(U-\Gamma\)(eV)	1.34	0.7	2.71	1.21	1.614	1.01
\({\Gamma }_{3}-\Gamma\)(eV)	2.14	1.0	1.78	1.91	2.068	1.156
Equivalent valleys
\(\Gamma\)	1
U	6
\({\Gamma }_{3}\)	1
\({\hslash \omega }_{LO}\)(meV)	0.091	0.099	0.073	0.093	0.087	0.094
\({D}_{ij}\)(eV m^-1)	10¹¹
\({\hslash \omega }_{ij}\)(meV)	0.073	0.099	0.029	0.078	0.06	0.085
\(\alpha\)(eV^-1) Nonparaboli-city
\(\Gamma\)	0.19	0.04	1.32	1.16	0.42	0.299
U	0.03	0	0.23	0.06	0.07	0.046
\({\Gamma }_{3}\)	0.08	0	0	0.023	0.061	0.0
\({P}_{z}\)(C/m²)	0.38	0.92	0.38	0.48	0.38	0.811

M: mass density \({v}_{s}\): Sound velocity, \({D}_{a}\): acoustic deformation potential, ɛ_s: static dielectric constant, \({\varepsilon }_{\infty }\): High Frequency dielectric constant, \({D}_{ij}\): Intervalley Deformation Potentials, \(\alpha\): non-parabolicity factor and \({P}_{z}\): piezoelectric constant are taken from reference^10,11.
m_ɼ: Effective mass at Γ valley, m_U: Effective mass at U valley, m_ɼ3: Effective mass at \({\Gamma }_{3}\) valley, \(U-\Gamma , {\Gamma }_{3}-\Gamma\) are valley separation, \({\hslash \omega }_{LO}\): Optical Phonon energies, \({\hslash \omega }_{ij}\): Intervalley Phonon Energies are extracted from the E–k data obtained through FullBand simulator.

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