{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bandgap Design\n",
    "A progressive documentation of a bangdap design in the Skywater 130 nm process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import SpiceInterface"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Investigate Process PNPs\n",
    "Let's begin by investigating the behaviour of the Skywater 130 nm 'sky130_fd_pr__pnp_05v5_W3p40L3p40' PNP devices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PNP IV Characteristics\n",
    "To start lets view the IV (Current/Voltage) relationship of the PNP device.\n",
    "\n",
    "This follows the well known Shockley diode equation:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ I_D = I_S \\left( e^{\\frac{V_D}{n V_T}} - 1 \\right) $\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; where $ V_T = \\frac{k T}{q} $\n",
    "\n",
    "This can be inverted to express the diode voltage:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ V_D = n V_T \\cdot ln \\left( \\frac{I_D}{I_S} + 1 \\right) $\n",
    "\n",
    "The logarithmic behaviour of the diode voltage with respect to current can clearly be seen below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "spice_interface_obj = SpiceInterface.SpiceInterface(netlist_path='bjt_test.spice', verbose=False)\n",
    "\n",
    "results = spice_interface_obj.sweep_parameter('ianode', 1e-6, 10e-6, 101, ['i(vvdd)', 'v(anode)'], \n",
    "                                                sweeptype='dcsweep')\n",
    "plt.plot([-_*1e6 for _ in results['i(vvdd)']], results['v(anode)'])\n",
    "\n",
    "plt.ylabel('voltage ($V$)')\n",
    "plt.xlabel('current ($\\mu A$)')\n",
    "plt.title('IV Curve of Skywater PNP')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $V_D$ Over Temperature\n",
    "We can see from the Shockley diode equation that the exponential term has a positive temperature coefficient in the $ V_T $ term. The higher the temperature the greater the voltage drop.\n",
    "\n",
    "However, when examining the temperature behaviour ($\\frac{\\partial V_D}{\\partial T}$) we see a negative temperature coefficient, often reffered to as Complimentary to Absolute Temperature (CTAT). The higher the temperature the lower the diode voltage. This behaviour can be seen below.\n",
    "\n",
    "###### Saturation Current Contribution\n",
    "Where does this surprising result come from? The answer is in the diodes saturation current, $I_S$. Which itself has a temperature coefficient.\n",
    "\n",
    "Expanding the Schockley diode equation further we find the expression for the saturation current is:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ {\\displaystyle I_{\\text{S}}=eAn_{\\text{i}}^{2}\\left({\\frac {1}{N_{\\text{D}}}}{\\sqrt {\\frac {D_{\\text{p}}}{\\tau _{\\text{p}}}}}+{\\frac {1}{N_{\\text{A}}}}{\\sqrt {\\frac {D_{\\text{n}}}{\\tau _{\\text{n}}}}}\\right)} $\n",
    "\n",
    "Here we start to see some of the fundamental parameters of semiconductor manufacturing such as doping concentrations, diffusion coefficients and carrier lifetimes.\n",
    "\n",
    "As the temperature rises the number of free carriers rises as every carrier in the device has a greater energy. This increase in conductivity leads to a lower voltage across the junction for a given foward current. Therefore, for a constant current the voltage of the diode junction reduces with rising temperature.\n",
    "\n",
    "\n",
    "MORE STUFF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = spice_interface_obj.sweep_parameter('temp', start=-40, end=125, number_steps=101,\n",
    "                                                signals=['v(anode)', 'temp'], sweeptype='dcsweep')\n",
    "\n",
    "plt.plot(results['temp'], results['v(anode)'])\n",
    "plt.xlabel('temperature ($^{\\circ} C$)')\n",
    "plt.ylabel('voltage ($V$)')\n",
    "plt.title('$V_{D}$ Over Temperature')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Difference of Diode Voltages\n",
    "Consider what the temperature coefficient of the difference of two diode voltages is. Of course, two identical diodes will have no voltage differences but if the diodes have different current densities something else occurs:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ V_\\Delta = n V_T \\cdot ln \\left( \\frac{I_{D_1}}{I_S} + 1 \\right) - n V_T \\cdot ln \\left( \\frac{I_{D_2}}{I_S} + 1 \\right) $\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ V_\\Delta = n V_T \\cdot \\left[ ln \\left( \\frac{I_{D_1}}{I_S} + 1 \\right) - ln \\left( \\frac{I_{D_2}}{I_S} + 1 \\right) \\right]$\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ V_\\Delta = n V_T \\cdot ln \\left( \\frac{\\frac{I_{D_1}}{I_S} + 1}{\\frac{I_{D_2}}{I_S} + 1} \\right) $\n",
    "\n",
    "As part of the design we ensure that the bias current is much greater than the saturation current and therefore the expression can be simplified to:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ V_\\Delta = n V_T \\cdot ln \\left( \\frac{\\frac{I_{D_1}}{I_S}}{\\frac{I_{D_2}}{I_S}} \\right) $\n",
    "\n",
    "We then ensure the two diodes are well matched leading to:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ V_\\Delta = n V_T \\cdot ln \\left( \\frac{I_{D_1}}{I_{D_2}} \\right) $\n",
    "\n",
    "Or more simply:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $ V_\\Delta = n V_T \\cdot ln \\left( A_M \\right) $\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; where $A_M$ is the ratio of current density of the diodes.\n",
    "\n",
    "Importantly the only temperature dependance now is in the $V_T$ term which is a postive temperature coefficient, or PTAT (Proportional To Absolute Temperature).\n",
    "\n",
    "\n",
    "The positive temperature coefficient is $kT$ or $\\frac{\\partial V}{\\partial T} \\approx +0.086~mV/K$. Compared with the negative temperature coefficient which is $\\approx -2~mV/K$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Combining PTAT and CTAT Sources\n",
    "Lets assume that the ratio of the current densities is 8. Then plot the temperature coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "This has been supported by the following material:\n",
    "\n",
    "['How to Make a Bandgap Voltage Reference in One Eeasy Lesson'](https://www.idt.com/eu/en/document/whp/how-make-bandgap-voltage-reference-one-easy-lesson-paul-brokaw) - A. Paul Brokaw\n",
    "\n",
    "['The Bandgap Reference'](http://www.seas.ucla.edu/brweb/papers/Journals/BRSummer16Bandgap.pdf) - B. Razavi\n",
    "\n",
    "['134N. Scaled bandage reference, adjustable voltage PVT independent references.'](https://www.youtube.com/watch?v=AMgrGvzCTck) - A. Hajimiri\n",
    "\n",
    "And of course, the mighty [Wikipedia](https://www.wikipedia.org)"
   ]
  }
 ],
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