bandgap-vs-dielectric.ipynb

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  {
   "cell_type": "markdown",
   "id": "d4cbe552-0c83-41b3-a023-6c248e7168d5",
   "metadata": {},
   "source": [
    "### Band gap vs dielectric constant analysis\n",
    "\n",
    "This code has been used to generate Fig 1 and Suppl. Fig. 1, for the manuscript \"The Defect Challenge of Wide-Bandgap Semiconductors for Photovoltaics and Beyond\".\n",
    "\n",
    "To run the notebook, you will need to install the following:\n",
    "\n",
    "- Python 3.8+\n",
    "- pymatgen\n",
    "- mpcontribs\n",
    "\n",
    "In addition, to use the Materials Project API and the MP Contribs API, you will need to generate API keys on the respective website.\n",
    "For more details see:\n",
    "\n",
    "- https://next-gen.materialsproject.org/api\n",
    "- https://contribs.materialsproject.org"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ahead-guitar",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Specs for https://contribs-api.materialsproject.org/apispec.json re-loaded from aHR0cHM6Ly9jb250cmlicy1hcGkubWF0ZXJpYWxzcHJvamVjdC5vcmcvYXBpc3BlYy5qc29u.\n"
     ]
    },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpcontribs.client import Client\n",
    "\n",
    "# replace with your API key from the MP Contribs website\n",
    "mp_contribs_api_key = \"XXXX\"\n",
    "\n",
    "client = Client(mp_contribs_api_key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c5934311-11cf-4e43-a7b9-54005c811190",
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tqdm.auto import tqdm\n",
    "\n",
    "query = {\n",
    "    \"project\": 'carrier_transport',\n",
    "    \"_limit\": 500,\n",
    "    \"_fields\": [\n",
    "        \"id\",\n",
    "        \"identifier\",\n",
    "        \"data.mₑᶜ.p.ε̄.value\",\n",
    "        \"data.mₑᶜ.p.ε₁.value\",\n",
    "        \"data.mₑᶜ.p.ε₂.value\",\n",
    "        \"data.mₑᶜ.p.ε₃.value\",\n",
    "        \"data.mₑᶜ.n.ε̄.value\",\n",
    "        \"data.mₑᶜ.n.ε₁.value\",\n",
    "        \"data.mₑᶜ.n.ε₂.value\",\n",
    "        \"data.mₑᶜ.n.ε₃.value\",\n",
    "    ],\n",
    "}\n",
    "\n",
    "def extract(result):\n",
    "    return {\n",
    "        d[\"identifier\"]: {\n",
    "            \"m_h\": d[\"data\"][\"mₑᶜ\"][\"p\"][\"ε̄\"][\"value\"],\n",
    "            \"m_e\": d[\"data\"][\"mₑᶜ\"][\"n\"][\"ε̄\"][\"value\"],\n",
    "            \"m_h1\": d[\"data\"][\"mₑᶜ\"][\"p\"][\"ε₁\"][\"value\"],\n",
    "            \"m_h2\": d[\"data\"][\"mₑᶜ\"][\"p\"][\"ε₂\"][\"value\"],\n",
    "            \"m_h3\": d[\"data\"][\"mₑᶜ\"][\"p\"][\"ε₃\"][\"value\"],\n",
    "            \"m_e1\": d[\"data\"][\"mₑᶜ\"][\"n\"][\"ε₁\"][\"value\"],\n",
    "            \"m_e2\": d[\"data\"][\"mₑᶜ\"][\"n\"][\"ε₂\"][\"value\"],\n",
    "            \"m_e3\": d[\"data\"][\"mₑᶜ\"][\"n\"][\"ε₃\"][\"value\"],\n",
    "        }\n",
    "        for d in result[\"data\"] if \"data\" in d\n",
    "    }\n",
    " \n",
    "result = client.contributions.get_entries(**query).result()\n",
    "\n",
    "data = extract(result)\n",
    "\n",
    "for page in tqdm(list(range(1, result[\"total_pages\"] + 1))):\n",
    "    result = client.contributions.get_entries(**query, page=page).result()\n",
    "    data.update(extract(result))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "improved-interview",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymatgen.ext.matproj import MPRester\n",
    "\n",
    "# replace with your API key from the Materials Project website.\n",
    "# Note this will be different from MP Contribs API key define above\n",
    "mp_api_key = \"XXXX\"\n",
    "\n",
    "mpr = MPRester(api_key=mp_api_key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "promotional-payday",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 31548/31548 [03:12<00:00, 163.70it/s]\n"
     ]
    }
   ],
   "source": [
    "# get cannonical MP ID for the transport calcs\n",
    "results = mpr.query({\"task_ids\": {\"$in\": list(data.keys())}}, properties=[\"task_id\", \"task_ids\"])\n",
    "mapping = {t: r[\"task_id\"] for r in results for t in r[\"task_ids\"]}\n",
    "data = {mapping[k]: v for k, v in data.items()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "hearing-alarm",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 31548/31548 [02:56<00:00, 179.16it/s]\n"
     ]
    }
   ],
   "source": [
    "results = mpr.query(\n",
    "    {\"task_id\": {\"$in\": list(data.keys())}},\n",
    "    properties=[\"band_gap.search_gap.band_gap\", \"diel.poly_electronic\", \"diel.poly_total\", \"task_id\", \"nelements\", \"pretty_formula\"]\n",
    ")\n",
    "\n",
    "for r in results:\n",
    "    data[r[\"task_id\"]][\"bandgap\"] = r[\"band_gap.search_gap.band_gap\"]\n",
    "    data[r[\"task_id\"]][\"eps_total\"] = r.get(\"diel.poly_total\")\n",
    "    data[r[\"task_id\"]][\"eps_inf\"] = r.get(\"diel.poly_electronic\")\n",
    "    data[r[\"task_id\"]][\"nelements\"] = r.get(\"nelements\")\n",
    "    data[r[\"task_id\"]][\"formula\"] = r.get(\"pretty_formula\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "peripheral-gospel",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame.from_records(data).T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cardiovascular-smoke",
   "metadata": {},
   "source": [
    "Filter very large effective masses and dielectric constants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "precise-nurse",
   "metadata": {},
   "outputs": [],
   "source": [
    "mask = (\n",
    "    (df[\"m_h\"] < 100) & \n",
    "    (df[\"m_e\"] < 500) & \n",
    "    (df[\"eps_total\"] < 500) & \n",
    "    (df[\"eps_inf\"] < 80)  & \n",
    "    (df[\"m_e\"] > 0.01)\n",
    ")\n",
    "df = df[mask]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4fae8f1-02e7-4ab8-9015-5209e5e9cc63",
   "metadata": {},
   "source": [
    "Get binary materials only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d68c58b9-fffb-4462-a52d-3d333fa7235c",
   "metadata": {},
   "outputs": [],
   "source": [
    "bin_df = df[~pd.isna(df[\"eps_inf\"])]\n",
    "bin_df = bin_df[bin_df[\"nelements\"] <= 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "dc7503fd-5df8-47cb-b34a-f57a764afeac",
   "metadata": {},
   "outputs": [
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       "<Figure size 273.6x432 with 3 Axes>"
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     "output_type": "display_data"
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   ],
   "source": [
    "import matplotlib\n",
    "from matplotlib import colors\n",
    "from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
    "from scipy.optimize import curve_fit\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "set_matplotlib_formats('svg')\n",
    "\n",
    "c1 = \"#A6DCEF\"\n",
    "c2 = \"#E36387\"\n",
    "lw = 0.3\n",
    "\n",
    "in_mask = (bin_df[\"bandgap\"] >= 1.6) & (bin_df[\"bandgap\"] <= 2.5)\n",
    "\n",
    "x1_in = bin_df[\"bandgap\"][in_mask]\n",
    "y1_in = bin_df[\"eps_inf\"][in_mask]\n",
    "x1_out = bin_df[\"bandgap\"][~in_mask]\n",
    "y1_out = bin_df[\"eps_inf\"][~in_mask]\n",
    "\n",
    "x2_in = bin_df[\"bandgap\"][in_mask]\n",
    "y2_in = bin_df[\"m_e\"][in_mask]\n",
    "x2_out = bin_df[\"bandgap\"][~in_mask]\n",
    "y2_out = bin_df[\"m_e\"][~in_mask]\n",
    "\n",
    "x3_in = bin_df[\"bandgap\"][in_mask]\n",
    "x3_out = bin_df[\"bandgap\"][~in_mask]\n",
    "y3_in = (1/bin_df[\"eps_inf\"][in_mask] -  1/bin_df[\"eps_total\"][in_mask])**2 * bin_df[\"m_e\"][in_mask]\n",
    "y3_out = (1/bin_df[\"eps_inf\"][~in_mask] -  1/bin_df[\"eps_total\"][~in_mask])**2 * bin_df[\"m_e\"][~in_mask]\n",
    "\n",
    "eps_func = lambda x, c: 1 / np.sqrt(c * x)\n",
    "c0 = curve_fit(eps_func, bin_df[\"bandgap\"].values.astype(float), bin_df[\"eps_inf\"].values.astype(float), bounds=[1e-32, 10])[0]\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(3, figsize=(3.8, 6), sharex=True)\n",
    "\n",
    "ax1.scatter(x1_out, y1_out, s=20, edgecolor=\"k\", linewidth=lw, c=c1)\n",
    "ax1.scatter(x1_in, y1_in, s=20, edgecolor=\"k\", linewidth=lw, c=c2)\n",
    "ax1.semilogy()\n",
    "xlim = ax1.get_xlim()\n",
    "ylim = ax1.get_ylim()\n",
    "ax1.set(ylabel=r\"$\\epsilon_\\infty$\", xlim=xlim, ylim=ylim)\n",
    "\n",
    "xs = np.linspace(0.0005, 10, 1000)\n",
    "ax1.plot(xs, eps_func(xs, c0), ls=\"--\", c=\"k\")\n",
    "ax1.text(0.95, 0.4, \"$\\epsilon_\\infty \\propto E_\\mathrm{g}^{-1/2}$\", ha=\"right\", va=\"bottom\", transform=ax1.transAxes, fontsize=12)\n",
    "\n",
    "scat = ax2.scatter(x2_out, y2_out, s=20, edgecolor=\"k\", linewidth=lw, c=c1)\n",
    "scat = ax2.scatter(x2_in, y2_in, s=20, edgecolor=\"k\", linewidth=lw, c=c2)\n",
    "ax2.semilogy()\n",
    "ax2.set(ylabel=r\"$m^*_\\mathrm{e}$ ($m_0$)\", ylim=(0.01, 500))\n",
    "\n",
    "ax3.scatter(x3_out, y3_out, s=20, edgecolor=\"k\", linewidth=lw, c=c1)\n",
    "ax3.scatter(x3_in, y3_in, s=20, edgecolor=\"k\", linewidth=lw, c=c2)\n",
    "ax3.semilogy()\n",
    "ax3.set(ylabel=r\"$m^*_\\mathrm{e} \\left( \\frac{1}{\\epsilon_\\infty} - \\frac{1}{\\epsilon_\\mathrm{s}} \\right)^2 $\", xlabel=\"Band gap (eV)\")\n",
    "\n",
    "\n",
    "alpha = 0.3\n",
    "ax1.axvspan(-1, 1.6, alpha=alpha, color='lightgrey',zorder=-1, linewidth=0)\n",
    "ax1.axvspan(1.6, 2.5, alpha=alpha, color=c2,zorder=-1, linewidth=0)\n",
    "ax1.axvspan(2.5, 10, alpha=alpha, color='lightgrey',zorder=-1, linewidth=0)\n",
    "\n",
    "ax2.axvspan(-1, 1.6, alpha=alpha, color='lightgrey',zorder=-1, linewidth=0)\n",
    "ax2.axvspan(1.6, 2.5, alpha=alpha, color=c2,zorder=-1, linewidth=0)\n",
    "ax2.axvspan(2.5, 10, alpha=alpha, color='lightgrey',zorder=-1, linewidth=0)\n",
    "\n",
    "ax3.axvspan(-1, 1.6, alpha=alpha, color='lightgrey',zorder=-1, linewidth=0)\n",
    "ax3.axvspan(1.6, 2.5, alpha=alpha, color=c2,zorder=-1, linewidth=0)\n",
    "ax3.axvspan(2.5, 10, alpha=alpha, color='lightgrey',zorder=-1, linewidth=0)\n",
    "\n",
    "plt.subplots_adjust(hspace=0.1)\n",
    "\n",
    "plt.savefig(\"fig1.pdf\", dpi=300, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "55e9f1bc-3315-4d83-a15c-eb08a8de7317",
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       "<Figure size 273.6x273.6 with 1 Axes>"
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   "source": [
    "c1 = \"#A6DCEF\"\n",
    "c2 = \"#E36387\"\n",
    "lw = 0.3\n",
    "\n",
    "in_mask = (bin_df[\"bandgap\"] >= 1.6) & (bin_df[\"bandgap\"] <= 2.5)\n",
    "\n",
    "x3_in = bin_df[\"bandgap\"][in_mask]\n",
    "x3_out = bin_df[\"bandgap\"][~in_mask]\n",
    "y3_in = bin_df[\"eps_total\"][in_mask] - bin_df[\"eps_inf\"][in_mask]\n",
    "y3_out = bin_df[\"eps_total\"][~in_mask] - bin_df[\"eps_inf\"][~in_mask]\n",
    "\n",
    "fig, ax3 = plt.subplots(figsize=(3.8, 3.8))\n",
    "\n",
    "ax3.scatter(x3_out, y3_out, s=20, edgecolor=\"k\", linewidth=lw, c=c1)\n",
    "ax3.scatter(x3_in, y3_in, s=20, edgecolor=\"k\", linewidth=lw, c=c2)\n",
    "ax3.semilogy()\n",
    "xlim = ax3.get_xlim()\n",
    "ax3.set(ylabel=r\"$\\epsilon_\\mathrm{s} - \\epsilon_\\infty$\",xlabel=\"Band gap (eV)\", xlim=xlim)\n",
    "\n",
    "alpha = 0.3\n",
    "ax3.axvspan(-1, 1.6, alpha=alpha, color='lightgrey',zorder=-1, linewidth=0)\n",
    "ax3.axvspan(1.6, 2.5, alpha=alpha, color=c2,zorder=-1, linewidth=0)\n",
    "ax3.axvspan(2.5, 10, alpha=alpha, color='lightgrey',zorder=-1, linewidth=0)\n",
    "\n",
    "plt.subplots_adjust(hspace=0.1)\n",
    "\n",
    "plt.savefig(\"figS1.pdf\", dpi=300, bbox_inches=\"tight\")"
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