questions about the BTE mobility theory

[maxwhite]

hello everyone:

i am working with the examples of https://docs.epw-code.org/doc/GaN-II.html on the mobility of polar materials.

But now i am quite confused by the BTE theory,
i want to know the physical meaning of the two parts shown in the paper formula 10 in paper:
"Hole mobility of strained GaN from first principles"-DOI: 10.1103/PhysRevB.100.085204

截屏2021-03-04 下午4.54.06.png (46.36 KiB) Viewed 36219 times

the first part including bloch band index nk,and the second part including e-p impact part
what exactly do they mean in physcis?

And I notice the mobility calculation increase with BTE calculation iteration increasing as shown in FIG

截屏2021-03-04 下午5.00.27.png (60.87 KiB) Viewed 36219 times

,why dose BTE contribution part increase the
mobility instead of decreasing?Does BTE calculation all increase with iteration increasing ?Or is this only
a coincidence?

Really appreciate you help!
Max

[sponce]

Dear Max,

Eq. 10 is the Boltzmann transport equation which is an equality in steady state between the driving force (i.e. the electric field) and the scattering (i.e. the electron-phonon scattering).

If you want to understand the physics behind, I can recommand the review https://iopscience.iop.org/article/10.1 ... b6a43/meta
In particular Eqs. 36 to 53.

Regarding your second question, you can see Eq. 39 that the conductivity (and therefore the mobility) is directly proportional to d_E f_nk (the Eq. 10 that you mention).

Therefore if you solve the BTE iteratively by adding the second term, you are effectively increasing d_E f_nk and therefore increasing the mobility.
As far as I know the self-consistent solution of the BTE will always give you a larger mobility than the SERTA one.

Hope this helps,
Samuel

[maxwhite]

Hi,
Samuel!

it really takes me sometime to figure out what's happening in BTE mobility theory!
I notice the satement from the paper you recommend
Rep. Prog. Phys. 83 (2020) 036501
below equation (50)
""The MRTA can be simplified even further if the rate for scattering back into the state |nk⟩ is neglected entirely."""
does it mean the scattering part of \tau_{mk+q->nk} is omitted in the SERTA omitting?(i really want to know the omitting part of SERTA!)

截屏2021-03-19 上午9.42.05.png (142.13 KiB) Viewed 36156 times

so the right two scattering parts <nk|*|mk+q> are omiiting ?