# Interpretation of overall mobility in terms of components in the LOG and transport files

Dear all,

I performed the constant relaxation time calculation. The following is my input for the settings.yaml file

doping: [-3E18, -6E18, -1E19, -3E19, -6.5E19, -8.5E19, -1E20, -1.25E20]
temperatures: [300,350,400,450,500,550,600,650,700,750,800,850,900]
constant_relaxation_time: 1.0E-14

# electronic_structure settings

interpolation_factor: 15
nworkers: 6

# material settings

deformation_potential: deformation.h5
elastic_constant:

• [ 81.755, 4.107, 40.109, 0.000, 0.000, -0.000 ]
• [ 4.107, 44.688, 4.478, 0.000, 0.000, -0.000 ]
• [ 40.109, 4.478, 74.337, 0.000, 0.000, -0.000 ]
• [ 0.000, 0.000, 0.000, 8.294, 0.000, 0.000 ]
• [ 0.000, 0.000, 0.000, 0.000, 54.796, 0.000 ]
• [ -0.000, -0.000, -0.000, 0.000, 0.000, -13.556 ]
high_frequency_dielectric:
• [29.057900, 0.000000, 0.000000]
• [0.000000, 16.006491, 0.000000]
• [0.000000, 0.000000, 46.797792]
pop_frequency: 0.32
static_dielectric:
• [29.06, 0, 0]
• [0, 23.76, 0]
• [0, 0, 46.80]
free_carrier_screening: true

# performance settings

mobility_rates_only: true
write_mesh: true
file_format: txt

The job was successfully done. But I am confused about how the overall mobilities are obtained, i.e., do they follow Matthiessen’s rule from the ADV, IMP, and POP parts? They do no strictly obey that rule to my checking.
Another question is how to average the tensor? For example, the obtained ADP is a tensor with small off-diagonal components. Then I got the averaged value by square root(squared xx-component+squared yy-component+squared zz-component), but such obtained one does not agree with the one in the LOG file.

Best,

Rundong

The mobility obtained using Matthiessen’s rule from the individual mobilities is only an estimate of the true mobility including all scattering mechanisms.

Instead of calculating mobility as 1/\mu = 1/\mu_{pop} + 1/\mu_{adp} + 1/\mu_{imp}, we instead calculate the overall electron lifetime as 1/\tau = 1/\tau_{pop} + 1/\tau_{adp} + 1/\mu_{imp}, and then compute the mobility using that.

In general, the mobility obtained using Matthiessen’s rule will be larger than the mobility obtained by summing the rates. Although, if there is a large difference in magnitude between POP, ADP and IMP then Matthiessen’s rule is a good approximation.

The average rate is obtained by averaging the eigenvalues of the mobility tensor at each doping and temperature. The eigenvalues will take into account non-diagonal elements of the tensor which you would observe in a polycrystalline sample (which averaging is trying to simulate).

Best,
Alex

Dear Alex,

Thanks for the clarification.

Best,
Rundong