The band structure of Silicon is calculated using the empirical tight-binding method implemented in the Python programming language. Only interactions between first nearest neighbors are taken into account. The energy splittings for Silicon at symmetry points appear to be somewhat accurate to accepted values, although second neighbors will have …

Tight-Binding Calculation of the Band Structure of Silicon.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "<h1>Tight-Binding Calculation of the Band Structure of Silicon</h1>\n",
    "<br> William M. Medlar <br>\n",
    "*Department of Physics, University of North Texas, Denton, Texas*\n",
    "<br><br> The band structure of Silicon is calculated using the empirical tight-binding method implemented in the Python programming language. <br> Only interactions between first nearest neighbors are taken into account. The energy splittings for Silicon at symmetry points appear <br> to be somewhat accurate to accepted values, although second neighbors will have to be examined for usable results.<br>\n",
    "    \n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. Introduction\n",
    "\n",
    "The tight-binding method is an attractive approach for its simplicity; it requires only a few empirical parameters to calculate a relatively accurate approximation of the band structure of a crystal. \n",
    "\n",
    "In this paper I will introduce the tight-binding method and the approximations it makes, and calculate a reasonably accurate band structure of Silicon with only six empirical parameters and the locations of a Silicon atom's nearest neighbors in real space. Calculated results are plotted and compared to accepted values and calculations from other empirical methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II. Tight-Binding Method\n",
    "\n",
    "The tight-binding method is so simple because it makes a number of approximations to get to that point. The name \"tight-binding\" comes from the approximation that \"core\" electrons -- electrons in filled orbitals --  are bound tightly to their nuclei. In the case of Silicon this corresponds to the $1s^2$, $2s^2$, and $2p^6$ orbitals, leaving the partially filled $3s$ and $3p$ shells as \"valence\" electrons. The tight-binding method ignores the contributions from the core electrons and instead focuses on the valence electrons, as they are responsible for bonding with other atoms.\n",
    "\n",
    "A second approximation that we make is the Born-Oppenheimer approximation -- simply that we can ignore the small kinetic contribution from the nuclei as they are significantly heavier than the electrons, and thus much slower.\n",
    "\n",
    "Our third approximation assumes that each electron in the atom experiences the same average potential $V(\\vec{r})$ -- the \"mean-field\" approximation.\n",
    "\n",
    "The tight-binding method approaches a crystal as a linear combination of the wavefunctions of isolated atoms, each with a single particle Hamiltonian of the form:\n",
    "\n",
    "$$\n",
    "H = H_{at} + \\Delta U\n",
    "$$\n",
    "\n",
    "where $\\Delta U$ contains the difference between the true potential of the crystal and the potential of the isolated atom. We assume that $\\Delta U \\rightarrow 0$ in the center of each atom. This gives single particle states of the form:\n",
    "\n",
    "$$\n",
    "H(\\vec{k}) \\Psi_{\\vec{k}}(\\vec{r}) = E_{\\vec{k}} \\Psi_{\\vec{k}}(\\vec{r})\n",
    "$$\n",
    "\n",
    "where $\\vec{k}$ is a wavevector in the first Brillouin zone. This single particle does not satisfy Bloch's theorem, however we can construct a linear combination of orbitals that do:\n",
    "\n",
    "$$\n",
    "\\psi_{\\vec{k}}(\\vec{r}) = \\frac{1}{\\sqrt{n}} \\sum\\limits_{\\vec{R}} e^{\\mathrm{i} \\: \\vec{k} \\cdot \\vec{R}} \\: \\phi(\\vec{r} - \\vec{R})\n",
    "$$\n",
    "\n",
    "where $\\vec{R}$ is a translation vector in real space and $\\phi(\\vec{r})$ is the atomic wavefunction that is an eigenstate of our earlier atomic Hamiltonian $H_{at}$. Our eigenfunctions of $H(\\vec{k})$ are given by:\n",
    "\n",
    "$$\n",
    "\\Psi(\\vec{k}) = \\sum\\limits_{i} C_i \\psi_i(\\vec{k})\n",
    "$$\n",
    "\n",
    "where our coefficients $C_i$ come from the minimization of the Rayleigh ratio. This leads to the eigenvalue problem:\n",
    "\n",
    "$$\n",
    "\\sum\\limits_{i,j} \\left( H_{i,j} - E(\\vec{k}) \\delta_{i,j} \\right) = 0\n",
    "$$\n",
    "\n",
    "For a Silicon basis of $3s$, $3p_x$, $3p_y$, $3p_z$ centered around each atom this will correspond to a matrix of the form:\n",
    "\n",
    "$$\n",
    "\\left(\n",
    "\\begin{array}{cccccccc}\n",
    "E_s & V_{ss} g_1 & 0 & 0 & 0 & V_{sp} g_2 & V_{sp} g_3 & V_{sp} g_4 \\\\\n",
    "V_{ss} g_1^* & E_s & -V_{sp} g_2^* & V_{sp} g_3^* & -V_{sp} g_4^* & 0 & 0 & 0 \\\\\n",
    "0 & -V_{sp} g_2 & E_p & 0 & 0 & V_{xx} g_1 & V_{xy} g_4 & V_{xy} g_2 \\\\\n",
    "0 & -V_{sp} g_3 & 0 & E_p & 0 & V_{xy} g_4 & V_{xx} g_1 & V_{xy} g_2 \\\\\n",
    "0 & -V_{sp} g_3 & 0 & 0 & E_p & V_{xy} g_2 & V_{xy} g_3 & V_{xx} g_1 \\\\\n",
    "V_{sp} g_2^* & 0 & V_{xx} g_1^* & V_{xy} g_4^* & V_{xy} g_2^* & E_p & 0 & 0 \\\\\n",
    "V_{sp} g_3^* & 0 & V_{xy} g_4^* & V_{xx} g_1^* & V_{xy} g_3^* & 0 & E_p & 0 \\\\\n",
    "V_{sp} g_4^* & 0 & V_{xy} g_2^* & V_{xy} g_2^* & V_{xx} g_1^* & 0 & 0 & E_p\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "where $g_n$ are functions of $\\vec{k}$ and the nearest neighbors $\\vec{d_n}$ given by:\n",
    "\n",
    "$$\n",
    "g_1(\\vec{k}) = \\frac{1}{4} \\left( e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_1}} + e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_2}} + e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_3}} + e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_4}}\\right) \\\\\n",
    "g_2(\\vec{k}) = \\frac{1}{4} \\left( e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_1}} + e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_2}} - e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_3}} - e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_4}}\\right) \\\\\n",
    "g_3(\\vec{k}) = \\frac{1}{4} \\left( e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_1}} - e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_2}} + e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_3}} - e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_4}}\\right) \\\\\n",
    "g_4(\\vec{k}) = \\frac{1}{4} \\left( e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_1}} - e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_2}} - e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_3}} + e^{\\mathrm{i} \\vec{k} \\cdot \\vec{d_4}}\\right)\n",
    "$$\n",
    "\n",
    "All that's left now is to calculate our eigenvalues."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III. Implementation\n",
    "\n",
    "Before we can build our matrix, we'll have to calculate our $g_n(\\vec{k})$ functions. These are complex scalars that adjust our potential parameters in elements where they are nonzero. The four definitions we have for $g_n(\\vec{k})$ can be condensed into one by making use of Python 3.5's new matrix multiplication operator, @."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def phase(k, neighbors):\n",
    "    '''\n",
    "    Determines phase factors of overlap parameters using the assumption that the\n",
    "    orbitals of each crystal overlap only with those of its nearest neighbor.\n",
    "    \n",
    "    args:\n",
    "        k: A numpy array of shape (3,) that represents the k-point at which to\n",
    "           calculate phase factors.\n",
    "        neighbors: A numpy array of shape (4, 3) that represents the four nearest\n",
    "                   neighbors in the lattice of an atom centered at (0, 0, 0).\n",
    "                   \n",
    "    returns:\n",
    "        A numpy array of shape (4,) containing the (complex) phase factors.\n",
    "    '''\n",
    "    \n",
    "    a, b, c, d = [np.exp(1j * k @ neighbor) for neighbor in neighbors]\n",
    "    factors = np.array([\n",
    "        a + b + c + d,\n",
    "        a + b - c - d,\n",
    "        a - b + c - d,\n",
    "        a - b - c + d\n",
    "    ])\n",
    "    return (1 / 4) * factors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the appropriate \"phase factors\" $g_n(\\vec{k})$ and empirical parameters we can build our Hamiltonian. This Hamiltonian is self-adjoint, thus $H = H^\\dagger$ and we should use the appropriate NumPy method, ```numpy.linalg.eigvalsh``` instead of ```eigvals``` to ensure we get real eigenvalues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def band_energies(g, es, ep, vss, vsp, vxx, vxy):\n",
    "    '''\n",
    "    Calculates the band energies (eigenvalues) of a material using the\n",
    "    tight-binding approximation for single nearest-neighbor interactions.\n",
    "    \n",
    "    args:\n",
    "        g: A numpy array of shape (4,) representing the phase factors with respect\n",
    "           to a wavevector k and the crystal's nearest neighbors.\n",
    "        es, ep, vss, vsp, vxx, vxy: Empirical parameters for orbital overlap\n",
    "                                    interactions between nearest neighbors.\n",
    "                                    \n",
    "    returns:\n",
    "        A numpy array of shape (8,) containing the eigenvalues of the\n",
    "        corresponding Hamiltonian.\n",
    "    '''\n",
    "    \n",
    "    gc = np.conjugate(g)\n",
    "\n",
    "    hamiltonian = np.array([\n",
    "        [         es,  vss * g[0],            0,            0,            0, vsp * g[1], vsp * g[2], vsp * g[3]],\n",
    "        [vss * gc[0],          es, -vsp * gc[1], -vsp * gc[2], -vsp * gc[3],          0,          0,          0],\n",
    "        [          0, -vsp * g[1],           ep,            0,            0, vxx * g[0], vxy * g[3], vxy * g[1]],\n",
    "        [          0, -vsp * g[2],            0,           ep,            0, vxy * g[3], vxx * g[0], vxy * g[1]],\n",
    "        [          0, -vsp * g[3],            0,            0,           ep, vxy * g[1], vxy * g[2], vxx * g[0]],\n",
    "        [vsp * gc[1],           0,  vxx * gc[0],  vxy * gc[3],  vxy * gc[1],         ep,         0,           0],\n",
    "        [vsp * gc[2],           0,  vxy * gc[3],  vxx * gc[0],  vxy * gc[2],          0,        ep,           0],\n",
    "        [vsp * gc[3],           0,  vxy * gc[1],  vxy * gc[1],  vxx * gc[0],          0,         0,          ep]\n",
    "    ])\n",
    "\n",
    "    eigvals = np.linalg.eigvalsh(hamiltonian)\n",
    "    eigvals.sort()\n",
    "    return eigvals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is the function we'll call to calculate our band structure across a path of k-points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def band_structure(params, neighbors, path):\n",
    "    \n",
    "    bands = []\n",
    "    \n",
    "    for k in np.vstack(path):\n",
    "        g = phase(k, neighbors)\n",
    "        eigvals = band_energies(g, *params)\n",
    "        bands.append(eigvals)\n",
    "        \n",
    "    return np.stack(bands, axis=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```linpath``` is a function taken from an earlier project of mine, and will be useful in creating a path of n k-points across the first Brillouin zone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def linpath(a, b, n=50, endpoint=True):\n",
    "    '''\n",
    "    Creates an array of n equally spaced points along the path a -> b, not inclusive.\n",
    "\n",
    "    args:\n",
    "        a: An iterable of numbers that represents the starting position.\n",
    "        b: An iterable of numbers that represents the ending position.\n",
    "        n: The integer number of sample points to calculate. Defaults to 50.\n",
    "        \n",
    "    returns:\n",
    "        A numpy array of shape (n, k) where k is the shortest length of either\n",
    "        iterable -- a or b.\n",
    "    '''\n",
    "    # list of n linear spacings between the start and end of each corresponding point\n",
    "    spacings = [np.linspace(start, end, num=n, endpoint=endpoint) for start, end in zip(a, b)]\n",
    "    \n",
    "    # stacks along their last axis, transforming a list of spacings into an array of points of len n\n",
    "    return np.stack(spacings, axis=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we set up our empirical parameters, from Chadi and Cohen$^2$. $E_s$ and $E_p$ are arbitrary as long as they obey $E_p - E_s = 7.20$. $E_s$ determines the zero of the energy, thus I've adjusted it so that the peak of the valence bands is set at 0, as is common convention.\n",
    "\n",
    "I've used 1000 sample k-points per path between symmetry points to get a very smooth graph. Diagonalizing an 8x8 matrix is a very quick task for a computer, so it doesn't hurt to push it a little."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Es, Ep, Vss, Vsp, Vxx, Vxy\n",
    "# Ep - Es = 7.20\n",
    "params = (-4.03, 3.17, -8.13, 5.88, 3.17, 7.51)\n",
    "\n",
    "# k-points per path\n",
    "n = 1000\n",
    "\n",
    "# lattice constant\n",
    "a = 1\n",
    "\n",
    "# nearest neighbors to atom at (0, 0, 0)\n",
    "neighbors = a / 4 *  np.array([\n",
    "    [1, 1, 1],\n",
    "    [1, -1, -1],\n",
    "    [-1, 1, -1],\n",
    "    [-1, -1, 1]\n",
    "])\n",
    "\n",
    "# symmetry points in the Brillouin zone\n",
    "G = 2 * np.pi / a * np.array([0, 0, 0])\n",
    "L = 2 * np.pi / a * np.array([1/2, 1/2, 1/2])\n",
    "K = 2 * np.pi / a * np.array([3/4, 3/4, 0])\n",
    "X = 2 * np.pi / a * np.array([0, 0, 1])\n",
    "W = 2 * np.pi / a * np.array([1, 1/2, 0])\n",
    "U = 2 * np.pi / a * np.array([1/4, 1/4, 1])\n",
    "\n",
    "# k-paths\n",
    "lambd = linpath(L, G, n, endpoint=False)\n",
    "delta = linpath(G, X, n, endpoint=False)\n",
    "x_uk = linpath(X, U, n // 4, endpoint=False)\n",
    "sigma = linpath(K, G, n, endpoint=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code will perform the actual calculation of the bands, along the conventional path $L \\rightarrow \\Gamma \\rightarrow X \\rightarrow U/K \\rightarrow \\Gamma$. Even with such a large value of n this shouldn't take longer than a second."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "bands = band_structure(params, neighbors, path=[lambd, delta, x_uk, sigma])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hopefully our plot is as lovely as the plot from the pseudopotential method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5wAAAJnCAYAAAD7kFy/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBON9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa75877b400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "plt.figure(figsize=(15, 9))\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "# remove plot borders\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['bottom'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.spines['left'].set_visible(False)\n",
    "\n",
    "# limit plot area to data\n",
    "plt.xlim(0, len(bands))\n",
    "plt.ylim(min(bands[0]) - 1, max(bands[7]) + 1)\n",
    "\n",
    "# custom tick names for k-points\n",
    "xticks = n * np.array([0, 0.5, 1, 1.5, 2, 2.25, 2.75, 3.25])\n",
    "plt.xticks(xticks, ('$L$', '$\\Lambda$', '$\\Gamma$', '$\\Delta$', '$X$', '$U,K$', '$\\Sigma$', '$\\Gamma$'), fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "\n",
    "# horizontal guide lines every 2.5 eV\n",
    "for y in np.arange(-25, 25, 2.5):\n",
    "    plt.axhline(y, ls='--', lw=0.3, color='black', alpha=0.3)\n",
    "\n",
    "# hide ticks, unnecessary with gridlines\n",
    "plt.tick_params(axis='both', which='both',\n",
    "                top='off', bottom='off', left='off', right='off',\n",
    "                labelbottom='on', labelleft='on', pad=5)\n",
    "\n",
    "plt.xlabel('k-Path', fontsize=20)\n",
    "plt.ylabel('Energy (eV)', fontsize=20)\n",
    "\n",
    "plt.text(1350, -18, 'Fig. 1. Band structure of Si.', fontsize=12)\n",
    "\n",
    "# tableau 10 in fractional (r, g, b)\n",
    "colors = 1 / 255 * np.array([\n",
    "    [31, 119, 180],\n",
    "    [255, 127, 14],\n",
    "    [44, 160, 44],\n",
    "    [214, 39, 40],\n",
    "    [148, 103, 189],\n",
    "    [140, 86, 75],\n",
    "    [227, 119, 194],\n",
    "    [127, 127, 127],\n",
    "    [188, 189, 34],\n",
    "    [23, 190, 207]\n",
    "])\n",
    "\n",
    "for band, color in zip(bands, colors):\n",
    "    plt.plot(band, lw=2.0, color=color)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV. Results\n",
    "\n",
    "As you can see our band structure is *smooth*, and very distinguishable. The valence bands show an unusually high degree of degeneracy, such that it makes it slightly difficult to differentiate each band without squinting. Comparing our band separations to Chadi and Cohen's$^2$ -- Fig. 2. -- you can see that they diverge quite significantly at several points, yet are quite accurate at others.\n",
    "\n",
    " | $\\Gamma_{25'}$ | $\\Gamma_{1}$ | $\\Gamma_{15}$ | $\\Gamma_{2'}$ | $L_{2'}$ | $L_1$ | $L_{3'}$ | $X_1$ | $X_4$ | $\\Sigma\\text{(0.5, 0.5, 0)}$ | $\\Sigma\\text{(0.7, 0.7, 0)}$\n",
    ":--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---:\n",
    "Calculated | 0 | -12.16 | 4.10 | 4.10 | -9.49 | -6.64 | -2.17 | -7.32 | -4.34 | -3.51 | -4.25\n",
    "Chadi and Cohen$^2$ | 0 | -12.16 | 3.42 | 4.10 | -9.44 | -7.11 | -1.44 | -7.70 | -2.87 | -3.84 | -4.32\n",
    "\n",
    "$$\\scriptsize \\text{Fig. 2. Energy splittings in eV at high-symmetry points of Silicon. Values are measured relative to } \\Gamma_{25'} \\text{.}$$\n",
    "\n",
    "Our bandgap was calculated to be $E_{gap}$ = 3.92 eV, significantly different from the literature value of 1.11 eV$^1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## V. Conclusion\n",
    "\n",
    "The physics behind the tight-binding method are far simpler than those of the pseudopotential method or density functional theory, however with the simplistic approximation comes weaker computational accuracy.\n",
    "\n",
    "Our unusual variations in separation energies are the consequence of leaving out second nearest-neighbor interactions, and are akin to a very crude approximation. To get accurate values, we will have to reconfigure our matrix to accept the second nearest-neighbor parameter that Chadi and Cohen put to use. As it stands, the tight-binding method with only first nearest-neighbors is a quaint exercise, but should not be used in calculations.\n",
    "\n",
    "That being said, this is a much less computationally taxing process than the pseudopotential method. If it were simple enough to implement interactions between second nearest-neighbors, the tight-binding method would be a prime candidate for approximating band structures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VI. References\n",
    "\n",
    "1. G. Pfanner, \"Tight-binding calculation of the band structure of Silicon,\" downloaded November, 2015\n",
    "2. D.J. Chadi and M.L. Cohen, \"Tight-binding calculations of the valence bands of diamond and zincblende crystals,\" phys. stat. sol. (b) 68, 405 (1975)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}

Thank you for posting this code. It has been very helpful in learning to write my own TB code. I noticed a mistake for those who may be using this as well. The value for Vxx in the paper by D. J. Chadi and L. Cohen is 1.71 not 3.17 (=Ep). This leads to a (slightly) more reasonable band gap of about 2.2 eV compared to 3.92 eV. The experimental value is about 1.1 eV for Silicon.