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"## Phonon-limited carrier mobility in semiconductors\n",
"\n",
"Author: S. Tiwari (v1, 06/01/2024)
\n",
"Revision: F. Giustino (v1.2, 07/03/2024)
\n",
"\n",
"In this Noteboook, we compute the phonon-limited carrier mobility of silicon using the _ab initio_ Boltzmann Transport Equation (BTE). Electrons and phonons are computed with Quantum ESPRESSO (QE), maximally-localized Wannier functions are computed with Wannier90, and transport properties are computed with EPW. "
]
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"Below we define constants that will remail unchanged throughout the Notebook. The object `silicon` is created as an instance of the `EPWpy` class. This object will contain everything that we need to execute and analyze the calculations."
]
},
{
"cell_type": "code",
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{
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"\n",
" \n",
" \n",
" -*#*- ...............- \n",
" .+*= .+%*-=%%: .=#*- -===============-:.\n",
" :*%=*%%- *%* #%* :+%+-%%+ .:. -=. :==-. \n",
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" :%%- -%S. \n",
" .-=*####SS%#########: -###########*+: +#######= =%SS####+::. \n",
" =+#**%SSSSSSSSSSSSSSSS= =SSSSSSSSSSSSSSS= #SSSSSSS*. +SSSSSSSS%%%%- \n",
" *%% =SSS.. .SSS= SSS=. .:+SSS+ -SSS:. .-::. .SSS+. #%* \n",
" #%#. =SSS. *S# *S%: SSS= %SS%. .SSS= #SSS%. :SSS: =%#. \n",
" *%%: =SSS#*#SSS- SSS= .+SSS+. %SS*.=SSSSS+ +SS%.:+%+ \n",
" +%%:=SSSSSSSSS- SSSSSSSSSSSSS=. +SSS:SSS%SSS:%SS*-#%= \n",
" ....#S==SSS:..SSS: =+- SSS%######+=. -SSS%SS%.#SS%SSS==%%=. \n",
" .:+##%%#*- =SSS. ::. :SSS. SSS=. SSSSSS:..SSSSSS: :*%%%*=- \n",
" #%+. -+#SSS*+++++++*SSS: .=+SSS#++++: %SSSS+. =SSSS%. :-+#%%+ \n",
" #%* .SSSSSSSSSSSSSSSSSS: *SSSSSSSSSSS. +SSS%. %SSS*. . .%%= \n",
" =%S :::::::::::::::::. .:::::::::. :::. :::. =+=-.#%+ \n",
" -%S: =+===#S: \n",
" ==*------------------------------=========+++++++++++++++++++++++========++-+## \n",
" =+++++++++++*******++++++++++++++++========------------------==========+++++++- \n",
"-- -- -- -- -- -- -- -- -- -- -- -- Structure Info -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
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"Retrieving SummaryDoc documents: 0%| | 0/1 [00:00, ?it/s]"
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"text": [
"lattice vector(1): [3.333573 0. 1.924639]\n",
"lattice vector(2): [1.111191 3.142924 1.924639]\n",
"lattice vector(3): [0. 0. 3.849278]\n",
"atom(1): Si [0.875 0.875 0.875]\n",
"atom(2): Si [0.125 0.125 0.125]\n",
"1\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Si/Si.upf\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Si/Si_r.upf\n",
"pseudo found at pseudodojo : ONCVPSP-PBE-FR-PDv0.4/Si_r.upf\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"Pseudopotential: Si_r.upf\n",
"Pseudopotential directory: '/mnt/storage/sabya/For_video/epwpy/notebooks_basic/pseudo/'\n",
"Prefix: si\n"
]
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"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import rc\n",
"import time, sys, os\n",
"import EPWpy\n",
"from EPWpy import EPWpy\n",
"from EPWpy.plotting import plot_bands\n",
"import plotly.io\n",
"plotly.io.renderers.default = \"sphinx_gallery\"\n",
"\n",
"silicon=EPWpy.EPWpy({'prefix':'si',\n",
" 'calculation':'\\'scf\\'',\n",
" 'structure_mp':\"mp-149\",\n",
" 'ecutwfc':'40', \n",
" 'celldm(1)':'10.262', \n",
" 'pseudo_auto':True, \n",
" },\n",
" env='mpirun')\n",
"silicon.run_serial=True\n",
"\n",
"\n",
"# Summary\n",
"\n",
"pseudopot=silicon.__dict__['pw_atomic_species']['pseudo'][0]\n",
"print('Pseudopotential:', silicon.__dict__['pw_atomic_species']['pseudo'][0])\n",
"print('Pseudopotential directory:', silicon.__dict__['pw_control']['pseudo_dir'])\n",
"print('Prefix:',silicon.__dict__['prefix'])\n",
"app = silicon.display_lattice(supercell=[2,2,1])\n",
"app.run()"
]
},
{
"cell_type": "markdown",
"id": "f654aca0",
"metadata": {},
"source": [
"### Self-consistent field (SCF) calculations\n",
"\n",
"Here we perform the self-consistent field calculation to obtain the electron charge density of silicon in the ground state. The calculation consists of three separate steps:\n",
"1. Apply the method `scf` to the object `silicon`. This step specifies runtime parameters for an SCF calculation on siicon \n",
"2. Based on the properties defined at step 1 as well as other properties that are set by default within EPWpy, the method `prepare` creates the input file needed by QE\n",
"3. The method `run` applied to the object `silicon` instructs QE to perform the SCF calculation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "ba5f9cea",
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- Calculation: scf -- -- -- -- -- -- -- -- -- -- -- \n",
"Running scf |████████████████████████████████████████| in 3.9s (0.42/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"silicon.scf(name='scf',kpoints={'kpoints':[[6,6,6]]})\n",
"silicon.prepare(1,type_run='scf')\n",
"silicon.run(4)\n",
"silicon.pw_util = silicon.PW_utilities()\n"
]
},
{
"cell_type": "markdown",
"id": "e3c8e276",
"metadata": {},
"source": [
"### Band structure calculation\n",
"\n",
"In this step, we compute the band structure of silicon along some high-symmetry lines in the Brillouin zone.\n",
"\n",
"This calculation is not strictly necessary to compute the mobility, but it is useful to understand the electronic structure of the system under consideration.\n",
"\n",
"Also in this case, we use **three instructions** to specify runtime parameters, prepare the input file, and execute the QE calculation."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "24a24c92",
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- Calculation: bs -- -- -- -- -- -- -- -- -- -- -- \n",
"Running bs |████████████████████████████████████████| in 4.7s (0.34/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"silicon.scf(control={'calculation':'\\'bands\\''},\n",
" system={'nbnd':12},\n",
" kpoints={'kpoints':[\n",
" ['0.5','0.50','0.50','20'],\n",
" ['0.0','0.00','0.00','20'],\n",
" ['0.5','0.25','0.75','20']\n",
" ],\n",
" 'kpoints_type':'{crystal_b}'\n",
" },\n",
" name='bs')\n",
"silicon.prepare(type_run='bs')\n",
"silicon.run(4,type_run='bs')"
]
},
{
"cell_type": "markdown",
"id": "44de2907",
"metadata": {},
"source": [
"### Band structure plot\n",
"\n",
"We now plot the electronic band structure computed at the previous step. The zero of the energy axis is set to the value specified manually via `ef0`.\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "9de61b52",
"metadata": {},
"outputs": [
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\n",
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