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Table 2 The formulas of major scattering mechanisms used in 2DEG mobility calculations

From: The role of dislocation-induced scattering in electronic transport in GaxIn1-xN alloys

Scattering mechanism Formula Definition of variables
Acoustic phonon: piezoelectric[1517] μ PE = π ε s 3 k e K 2 k B T m * 2 1 J PE k K, electromagnetic coupling coefficient; JPE(k), electron wave vector dependent integral.
J PE k = 0 2 k F 11 q 4 k 2 q + q s 2 1 q / 2 k 2 q 3 d q
K 2 = ε LA 2 ε s c LA + ε TA 2 ε s c TA
Acoustic phonon: deformation[11, 18] potential μ DP = 16 ρ e v s 2 3 3 Ξ 2 k B T m * 2 b 1 J DP k ρ, crystal density; v s , longitudinal acoustic phonon velocity; Ξ, deformation potential constant; m*, electron effective mass; JDP(k), electron wave vector dependent integral. b, Fang-Howard expression; qs, reciprocal screening length; f(0), occupation probability; F11(q), ground-state Fang-Howard wave function.
J DP k = 0 2 k 1 2 k π 3 q + q s 2 1 q / 2 k 2 q 4 d q
q s = e 2 m * 2 π 2 ε s F 11 q f 0
b = 33 e 2 m * n 2 D 8 ε s 2 1 / 3
F q = b 8 b 2 + 9 q b + 3 q 2 / 8 b + q 3
Polar optical phonon[1719] μ PO = 4 π ε s 2 e ω m * 2 Z 0 e ω LO / k B T 1 ω LO , polar optical phonon energy; ε and ε s , high- and low-frequency dielectric constant; Z0, effective width of triangular well formed at the GaxIn1-xN/GaN interface and is given in terms of Fermi wave vector.
1 ε P = 1 ε 1 ε s
Z 0 = 2 π k F = 2 π n 2 D
Interface roughness[11, 15, 20] μ IFR = 2 ε s n 2 D Δ Λ 2 3 e 3 m * 2 1 J IFR k Δ, lateral size of the roughness; Λ, correlation length between fluctuations; JIFR(k), correlation length and the lateral size-dependent integral; n2D, 2D electron density.
J IFR k = 0 2 k exp q 2 Λ 2 / 4 2 k 3 q + q s 2 1 q / 2 k 2 q 4 d q
q = 2 k sin θ / 2
q s = e 2 m * 2 π ε s 2 F q
Alloy disorder[20] μ Alloy = 16 e 3 3 b x 1 x m * 2 Ω 0 U A 2 x, Ga fraction; Ω0, the volume occupied by one atom; UA, alloy potential.
Dislocation[2123] μ Dis = 30 2 π ε 2 c 2 k B T 3 / 2 e 3 N Dis f 2 λ D m * NDis, dislocation density per unit area which is taken as a fitting parameter; λD, Debye screening length; c, lattice constant of GaxIn1-xN. f, the fraction of filled traps that are assumed fully occupied.
  λ D = ε s k B T / e 2 n 2 D 1 / 2