A Model of Numerical Calculation of Conductivity for III-V MBE Epilayers Using a Hall Device

Table 1

Scattering mechanisms used in calculations.

Semiconductor	Scattering on ionized donors and acceptors	Scattering on acoustic phonons (deformation potential)	Scattering on acoustic phonons (piezoelectric potential)	Scattering on optics polar phonons	Scattering on space charge	Scattering on dislocations
InAs	𝜏ii=𝑎𝑏; 𝑎=5.332⋅10^7𝜀^2𝑟𝑚^0,5ef,𝑛,𝑝𝑒𝑝𝑠^1.925; 𝑏=𝑁𝐼𝑍^2−𝑦ln1+𝑦1+𝑦; 𝑦=3.145⋅10^36𝑚ef,(𝑛,𝑝)𝜀𝑟𝑇𝑛,𝑝𝑒𝑝𝑠; 𝑁𝐼=𝑛+2⋅𝑝; 𝑍=1	𝜏dp=3.012⋅10^−12𝑇⋅𝑚^1.5ef,(𝑛,𝑝)𝑒𝑝𝑠^0.5	𝜏pie=9.502⋅10^−8𝑒𝑝𝑠/𝑚ef,(𝑛,𝑝)𝑇^2(ℎ14)^2((3/𝐶𝑙)+(4/𝐶𝑡))	𝜏po=0.02781⋅𝑓𝑇⋅𝑒𝑝𝑠^0.5stdi⋅𝑚^0.5ef,𝑛,𝑝; 𝑇𝐷=337−9.1156(𝑇−4.75555)^1.1179; ×exp−𝑇−11.19615.781; 𝑓𝑇1=1−0.5841𝑇𝐷𝑇+0.292𝑇𝐷𝑇^2; −0.037164𝑇𝐷𝑇^3+0.0012𝑇𝐷𝑇^4; 𝑓𝑇2=8^−13√𝜋𝑇𝐷𝑇; 𝑓𝑇3=iF𝑇<84,𝑓𝑇2,𝑓𝑇1; 𝑓𝑇=exp𝑇𝐷𝑇−1𝑓𝑇3; 1stdi=𝜀opt𝜀0−1𝜀𝑟𝜀0	𝜏SC=𝑚ef(𝑛,𝑝)⋅9.108⋅10^−28𝑁𝑠𝑄⋅√𝑒𝑝𝑠
In0.53Ga0.47As	𝜏ii=𝑎𝑏; 𝑎=5.332⋅10^7𝜀^2𝑟𝑚^0.5ef,(𝑛,𝑝)𝑒𝑝𝑠^2.8; 𝑏=𝑁𝐼𝑍^2−𝑦ln1+𝑦1+𝑦; 𝑦=3.145⋅10^36𝑚ef,(𝑛,𝑝)𝜀𝑟𝑇𝑛,𝑝𝑒𝑝𝑠; 𝑁𝐼=𝑛+2⋅𝑝; 𝑍=1	𝜏dp=3.012⋅10^−12𝑇⋅𝑚^1.5ef,(𝑛,𝑝)𝑒𝑝𝑠^0.5	𝜏pie=9.502⋅10^−8𝑒𝑝𝑠/𝑚ef,(𝑛,𝑝)𝑇^2(ℎ14)^2((3/𝐶𝑙)+(4/𝐶𝑡))	𝜏po=0.02781⋅𝑓𝑇⋅𝑒𝑝𝑠^0.5stdi⋅𝑚^0.5ef,(𝑛,𝑝); 𝑇𝐷=358.44−9.1156(𝑇−4.75555)^1.1179; ×exp−𝑇−11.19615.781; 𝑓𝑇1=1−0.5841𝑇𝐷𝑇+0.292𝑇𝐷𝑇^2; −0.037164𝑇𝐷𝑇^3+0.0012𝑇𝐷𝑇^4; 𝑓𝑇2=8^−13√𝜋𝑇𝐷𝑇; 𝑓𝑇3=iF[𝑇<84,𝑓𝑇2,𝑓𝑇1]; 𝑓𝑇=[exp𝑇𝐷𝑇−1]𝑓𝑇3; 1stdi=𝜀opt𝜀0−1𝜀𝑟𝜀0	𝜏SC=𝑚ef(𝑛,𝑝)⋅9.108⋅10^−28𝑁𝑠𝑄⋅√𝑒𝑝𝑠	𝜏disl=9.082⋅10^2𝑚ef(𝑛,𝑝)𝑇^0.44√𝑘
GaAs	𝜏ii=𝑎𝑏; 𝑎=5.332⋅10^7𝜀^2𝑟𝑚^0.5ef,(𝑛,𝑝)𝑒𝑝𝑠^1.91; 𝑏=𝑁𝐼𝑍^2−𝑦ln1+𝑦1+𝑦; 𝑦=3.145⋅10^36𝑚ef,(𝑛,𝑝)𝜀𝑟𝑇𝑛,𝑝𝑒𝑝𝑠; 𝑁𝐼=𝑛+2⋅𝑝; 𝑍=1			𝜏po=0.02781⋅𝑓𝑇⋅𝑒𝑝𝑠^0.35stdi⋅𝑚^0.5ef,(𝑛,𝑝); 𝑇𝐷=358.44−9.1156(𝑇−4.75555)^1.1179; ×exp−𝑇−11.19615.781; 𝑓𝑇1=1−0.5841𝑇𝐷𝑇+0.292𝑇𝐷𝑇^2; −0.037164𝑇𝐷𝑇^3+0.0012𝑇𝐷𝑇^4; 𝑓𝑇2=8^−13√𝜋𝑇𝐷𝑇; 𝑓𝑇3=iF𝑇<84,𝑓𝑇2,𝑓𝑇1; 𝑓𝑇=[exp𝑇𝐷𝑇−1]𝑓𝑇3; 1stdi=𝜀opt𝜀0−1𝜀𝑟𝜀0	𝜏SC=𝑚ef(𝑛,𝑝)⋅9.108⋅10^−28𝑁𝑠𝑄⋅√𝑒𝑝𝑠