band-structre_and_DOS_Si.ipynb

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   "source": [
    "# 5.3. Ejemplo 3. Estructura de Bandas y Densidad de Estados para celda de silicio.\n",
    "\n",
    "La estructura de bandas del silicio cristalino (estructura tipo diamante), es bien conocida, por lo en este notebook se utilizará dicho sistema como ejemplo para obtener con QE una estructura de bandas de un material semiconductor, así como su densidad de estados (DOS). El ejercicio está dividido en 4 partes:\n",
    "\n",
    "0. **Ejercicio 4** de convergencia de *ecutwfc* y *kpoints* para el Si.\n",
    "1. Cálculo de SCF.\n",
    "2. Cálculo de bandas y post procesamiento de bandas.\n",
    "3. **Ejercicio 5**, cálculo de densidad de estados y post procesamiento. "
   ]
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   "source": [
    "## 2. SCF\n",
    "\n",
    "Generar un archivo de entrada para correr un cálculo tipo \"*scf*\". Con los resultados del $\\textbf{ejercicio 4}$ -de convergencia-, sustituir el $\\textit{ecutwfc}$ y la red de $\\textit{k-points}$ adecuada en el siguiente archivo y generamos el archivo de entrada para el cálculo de autoconsistencia o $\\textit{scf}$. \n",
    "\n",
    "E.g.:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"./Figs/PSSi-scf.in.png\" style=\"width: 600px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilizando la red de Bravais $\\textbf{fcc}$ (que en QE corresponde a $\\textit{ibrav = 2}$), colocando 2 átomos de de silicio en las posiciones indicadas, se reproduce la estructura tipo diamante del silicio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "% more SiBandStructure/Si.in"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con el siguiente comando escrito en la terminal se puede ver la estructura con el software XCrysDen:\n",
    "*xcrysden --pwi Si.in*.\n",
    "O bien, abriendo *XCrySDen* y desde ahí, abriendo el archivo [Si-scf.in](SiBandStructure/Si-scf.in)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La estructura en su plano XY y en perspectiva es la siguiente:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<tr>\n",
    "<td> <img src=\"./Figs/Sixy.png\" style=\"width: 300px\"> \n",
    "<td> <img src=\"./Figs/Siiso.png\" style=\"width: 300px\">\n",
    "<tr>\n",
    "\n",
    "**Figura:** Visualización de la estructura de silicio tipo diamante con *XCrySDen*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para correr este *input* utilizamos el mismo ejecutable $\\textbf{pw.x}$ que ya introdujimos en la sección anterior, obteniendo el archivo de salida [Si.out](SiBandStructure/Si.out):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: The following floating-point exceptions are signalling: IEEE_DENORMAL\r\n",
      "Note: The following floating-point exceptions are signalling: IEEE_DENORMAL\r\n"
     ]
    }
   ],
   "source": [
    "!mpirun --np 2 /qe-6.3/bin/pw.x < ./SiBandStructure/Si.in > ./SiBandStructure/Si.out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Estructura de bandas\n",
    "En el archivo de salida podemos observar variables como la energía total del sistema, el número de $\\textit{kpoints}$ utilizados, etc.\n",
    "Sin embargo ahora nos interesa graficar la estructura de bandas del silicio, para lo cual se requiere modificar el archivo [*Si.in*](SiBandStructure/Si.in) y generar un archivo suplementario $\\textbf{bandas.in}$.\n",
    "\n",
    "En el archivo *Si.in* se cambia el cálculo de *scf* a *bands* y se modifica la sección de los *K_POINTS* de la siguiente manera:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"./Figs/PSSi_bands.in.png\" style=\"width: 600px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La sección de los *k-points*, indicando las coordenadas en la red recíproca de 6 de ellos, responde a que la trayectoria entre estos - W, $\\Gamma$, X, L y regresando a $\\Gamma$-, es una trayectoria de alta simetría como se aprecia en la siguiente figura. Las trayectorias de alta simetría contienen información de máximos y mínimos de bandas del sistema. \n",
    "\n",
    "<tr>\n",
    "<td> <img src=\"./Figs/fcc-RLC.PNG\" style=\"width: 300px\">\n",
    "<img src=\"./Figs/fcc-RLC-path.PNG\" style=\"width: 400px\">\n",
    "<tr>\n",
    "\n",
    "**Figura.** Espacio recíproco de la celda de silicio, puntos y trayectoria de alta simetría.  Ref: [Sertwayan et. al 2010.](Docs/Sertwayan_Curtarolo_CMS2010.pdf) Además de esta referencia, puede ser de utilidad la siguiente página web: http://lampx.tugraz.at/~hadley/ss1/bzones/fcc.php en donde también se muestra la red reciproca, la celda de Brillouin de la celda fcc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con lo cual especificamos que se realizará un cálculo de los eigenvalores para cada bandas específicamente en el recorrido indicado, del punto W al $\\Gamma$, X, W, L y $\\Gamma$. Es importante cambiar *{automatic}* a *{crystal_b}* e indicar tanto el número de puntos de alta simetría, como el número de puntos con el que se mapeará la trayectoria lineal en el espacio recíproco entre ellos -30 puntos-. \n",
    "\n",
    "Teniendo esto, se corre la instrucción:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
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   },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: The following floating-point exceptions are signalling: IEEE_DENORMAL\r\n",
      "Note: The following floating-point exceptions are signalling: IEEE_DENORMAL\r\n"
     ]
    }
   ],
   "source": [
    "!mpirun --np 2 /qe-6.3/bin/pw.x < ./SiBandStructure/Si.in > ./SiBandStructure/Sibands.out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esto genera las funciones de onda en los kpoints indicados, para este caso cerca de 150 funciones de onda (que se guardan en una nueva carpeta si.save). \n",
    "Posteriormente se corre la siguiente instrucción -que únicamente realiza tareas de postprocesamiento- con el archivo de PP [bands.in](SiBandStructure/bands.in)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"./Figs/PSbands.in.png\" style=\"width: 600px\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: The following floating-point exceptions are signalling:Note: The following floating-point exceptions are signalling: IEEE_OVERFLOW_FLAG IEEE_DENORMAL\r\n",
      " IEEE_OVERFLOW_FLAG IEEE_DENORMAL\r\n",
      "Note: The following floating-point exceptions are signalling: IEEE_OVERFLOW_FLAG IEEE_DENORMAL\r\n",
      "Note: The following floating-point exceptions are signalling: IEEE_OVERFLOW_FLAG IEEE_DENORMAL\r\n"
     ]
    }
   ],
   "source": [
    "!mpirun --np 4 /qe-6.3/bin/bands.x < ./SiBandStructure/bands.in> ./SiBandStructure/Bands.out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esto genera varios archivos: si.xml, 4 archivos si.wfc# -por haber utilizado 4 procesadores-, archivos que contienen funciones de onda, Bandx.dat.gnu, Bandx.dat, Bandx.dat.rap y una carpeta si.save que contiene archivos wfc#.dat con información de la función de onda, así como los archivos charge-density.dat, data-file.schema.xml y Si.pz-vbc.UPF. Toda esta información permite hacer análisis muy detallados de las las diferentes bandas, densidades electrónicas, etc. \n",
    "\n",
    "En particular el archivo [*Bandx.dat.gnu*](Bandx.dat.gnu), es de gran utilidad para hacer gráficas de estructura de bandas. Es un archivo de 2 columnas y una serie de bloques en donde la primera columna representa el recorrido que fijamos en el espacio recíproco ($\\textit{kpoints}$) y la segunda columna, cada una de las bandas, ordenadas de la más negativa o interna, cercana a los núcleos, hasta la más externa o lejana en la banda de conducción. \n",
    "Dicho documento puede graficarse rápidamente, *x* vs *y*, de la siguiente manera."
   ]
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s2mNL4ZzSN4yPbhzd5IzcahXYdbKS1fvy2JBWgskiMCw+iGtHxzN7WHSrVVab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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2c1ef8a908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd #importar libreria para trabajar con data frames. \n",
    "import numpy as np #importar librería para trabajar vectores y matrices. Su objeto mas importante es el Array\n",
    "import matplotlib.pyplot as plt\n",
    "import pylab\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "bsgnu = pd.read_table('./Bandx.dat.gnu',delim_whitespace=True, names=('kpoint', 'eigen')) #Leer el archibo Bandx.dat.gnu y asignarlo a una tabla\n",
    "\n",
    "#bs \n",
    "\n",
    "bsdata=pd.DataFrame(bsgnu) # definimos un data frame para hacer operaciones\n",
    "\n",
    "filas=bsdata.shape[0] #numero de filas\n",
    "\n",
    "i=1     #para obtener el número de kpoints contamos hasta que encontremos otro igual al primero\n",
    "kpoint1=bsdata.loc[0,'kpoint']\n",
    "while bsdata.loc[i,'kpoint']!=kpoint1:\n",
    "    i=i+1  \n",
    "N_kps=i      #numero de kpoints\n",
    "Nbands=filas/N_kps    #numero de bandas\n",
    "\n",
    "bsdata.loc[[],['kpoint','eigen']]\n",
    "plt.plot(bsdata['kpoint'],bsdata['eigen'])\n",
    "#bs[[]]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En la gráfica de arriba se observa una  estructura de bandas adecuada correcta, pero con el siguiente código en Phyton se puede obtener una gráfica más clara, la típica gráfica de estructura de bandas del silicio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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y5Txz5gyjoqK4Z88eTpw4kT4+PgTA0NDQfJaH3333HQFw5syZBZb/4jOsVCrFdaoPPvjA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2c1eb6b518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Este texto fue escrito por Levi Lentz en MIT y modificado por Felipe Cervantes de Ibero.\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.gridspec as gs\n",
    "import pylab\n",
    "import sys\n",
    "\n",
    "#Función para obtener los puntos de alta simetria del archivo *.out.\n",
    "def Symmetries(fstring): \n",
    "    f = open(fstring,'r')\n",
    "    x = np.zeros(0)\n",
    "    for i in f:\n",
    "        if \"high-symmetry\" in i:\n",
    "            x = np.append(x,float(i.split()[-1]))\n",
    "    f.close()\n",
    "    return x\n",
    "# Esta función lee el archivo *.dat.gnu, se le da una energía de fermi, lee el archivo de simetría y un \"nombre\"\n",
    "# Extrae los datos de las bandas del archivo *.dat.gnu  y grafica las bandas, con un shift dejando el cero en la \n",
    "#energía de fermi y marca los puntos kpoints de alta simetría.\n",
    "\n",
    "def bndplot(datafile,fermi,symmetryfile,label):\n",
    "    z = np.loadtxt(datafile) #se asigna a z el archivo Bandx.dat.gnu \n",
    "    x = np.unique(z[:,0]) # Lee y asigna a x todos los puntos kpoints unicos. \n",
    "    bands = []   # generamos un arreglo vacío\n",
    "    bndl = len(z[z[:,0]==x[1]]) # Se define el número de bandas como longitud de las veces en que los kpoints se repiten\n",
    "    Fermi = float(fermi)       # Cambiar Fermi a float\n",
    "    z[:,1]=z[:,1]-Fermi     # restamos Fermi para tener Fermi en cero\n",
    "    axis = [min(x),max(x),-12, 12]  #definimos los ejes. \n",
    "    for i in range(0,bndl):    \n",
    "        bands.append(np.zeros([len(x),2])) # Generamos una matriz de ceros donde se almacenarán las bandas \n",
    "    for i in range(0,len(x)):\n",
    "        sel = z[z[:,0] == x[i]]  # Aquí estan las energías para un punto x de los kpoints\n",
    "        for j in range(0,bndl): # Este ciclo separa las cada una de las bandas en j valores\n",
    "            bands[j][i][0] = x[i]\n",
    "            bands[j][i][1] = np.multiply(sel[j][1],1)  #bands[j][i][k] para k = 0 , bands[j][n]==bands[j][m], el resultado es un kpoint\n",
    "                                                        # para k = 1, j e i definen la banda y el kpoint, el resultado es un eigenvalor. \n",
    "    fff=np.shape(bands)\n",
    "    for i in bands: # Aquí se grafican las bandas\n",
    "        plt.plot(i[:,0],i[:,1],color=\"black\")\n",
    "    temp = Symmetries(symmetryfile) # Se llama a la función que busca puntos de alta simetria kpoints.\n",
    "    for j in temp: # En este ciclo se grafican las lineas tenues para los puntos \n",
    "        x1 = [j,j]\n",
    "        x2 = [axis[2],axis[3]]\n",
    "        plt.plot(x1,x2,'--',lw=0.55,color='black',alpha=0.75)\n",
    "    plt.plot([min(x),max(x)],[Fermi-Fermi,Fermi-Fermi],color='red',)\n",
    "    plt.xlabel('K-point')\n",
    "    plt.ylabel('Energy -E_f(eV)')\n",
    "    plt.ylim([axis[2],axis[3]])\n",
    "    plt.xlim([axis[0],axis[1]])\n",
    "    plt.xticks([])\n",
    "    plt.text((axis[1]-axis[0])/2.0,axis[3]+0.8,label,va='center',ha='center',fontsize=15)\n",
    "    plt.show()\n",
    "\n",
    "#! Importante incluir en la siguiente línea los datos de entrada de la función bndplot\n",
    "bndplot('./Bandx.dat.gnu',6.1673,'./SiBandStructure/Bands.out','Silicon')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso la estructura de está graficada con un corrimiento de la Energía de Fermi a cero, se marcan con líneas punteadas los puntos *kpoints* de alta simetría e indicamos los ejes y el título. \n",
    "Dicha gráfica se puede comparar con las reportadas en la [literatura](http://cmt.dur.ac.uk/sjc/thesis/thesis/node39.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. *Density of States DOS* del silicio.\n",
    "\n",
    "Al igual que para obtener la estructura de bandas, el procedimiento para obtener la densidad de estados involucra un post-procesamiento de los datos. \n",
    "\n",
    "El último **ejercicio 5** de este documento es graficar la densidad de estados del silicio, a continuación se proporcionan algunos *hints*.\n",
    "\n",
    "* Con calculation: *nscf* y una malla de kpoint densa, correr:\n",
    "    * mpirun --np 2 /qe-6.3/bin/pw.x < si-test3.dos.in > si-test3.dos.out\n",
    "\n",
    "* Construir un archivo auxiliar **dos.in**."
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    "* Correr el archivo auxiliar con el código de PP dos.x:\n",
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    "**Nota:**\n",
    "\n",
    "Para estructuras con polarización de spin, es necesario incluir una instrucción extra en el archivo **bands.in**: *spin_component=1*, realizar el cálculo de postprocesamiento y luego repetir para *spin_component=2*. Los resultados se deben salvar en archivos independientes para poder posteriormente tener los archivos correspondientes a *spin up* y *spin down*, 1 y 2 respectivamente. (PP/Docs/INPUT_BANDS.txt)."
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    "\n",
    "[Trabajo a Futuro, conclusiones y agradecimientos](Conclusiones.ipynb)\n",
    "\n",
    "[Ir al notebook anterior.](SiRelax.ipynb)\n"
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