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    "# ECE 606 Lecture 6.1: Electron tunneling — the transfer matrix method\n",
    "\n",
    "*From* [Nanoelectronic Modeling — From Atoms to Devices](https://nanohub.org/resources/45001), *Gerhard Klimeck, Purdue University. Lecture page:* [nanoHUB resource 37106](https://nanohub.org/resources/37106) — [video](https://nanohub.org/resources/37799) · [slides](https://nanohub.org/resources/37798) · [YouTube](https://youtube.com/watch?v=KeXDKgcKawE)\n",
    "\n",
    "**In this lecture**\n",
    "\n",
    "- where Section 6 starts: the closed-system recipe of Section 5 (ansatz, edge conditions, interface conditions, determinant, normalization) and what changes for an open system\n",
    "- a single barrier as a scattering problem: an incident wave A, a reflected wave B, a transmitted wave E, and no wave F coming in from the right\n",
    "- the wave in each region: plane waves where the electron is above the band edge, growing and decaying exponentials inside the barrier\n",
    "- the interface conditions written as 2×2 matrices M₁ and M₂, and their product, the transfer matrix\n",
    "- the general transfer-matrix method for any stack of layers, conceptually simple but with numerical limits\n",
    "\n",
    "**In this notebook** builds the interface matrices of the slides in a few lines of numpy, checks them against a general transfer-matrix code, and compares both with open-nemo's transmission, which comes from a discretized Schrödinger equation with open boundary conditions. It then rebuilds the wave function inside a barrier from the coefficients and compares it with open-nemo's injected density, and ends with a first look at why the method is said to have numerical issues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7e789a6d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:04.498790Z",
     "iopub.status.busy": "2026-10-25T17:49:04.498548Z",
     "iopub.status.idle": "2026-10-25T17:49:05.123502Z",
     "shell.execute_reply": "2026-10-25T17:49:05.123055Z"
    }
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   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import opennemo as nemo\n",
    "from opennemo.visualization import style\n",
    "\n",
    "style.use(notebook=True)\n",
    "H2M0 = nemo.core.units.HBAR2_2M0          # ħ²/2m₀ = 0.0381 eV nm²\n",
    "EM = nemo.structures.materials.EffectiveMassMaterial"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c6d9e38",
   "metadata": {},
   "source": [
    "## 1. From a closed box to an open system\n",
    "\n",
    "Section 5 solved closed problems: an electron in an infinite or finite well. The recipe had five steps:\n",
    "\n",
    "1. write a solution ansatz in each of the $N$ regions of constant potential ($2N$ unknown coefficients),\n",
    "2. impose $\\psi(\\pm\\infty) = 0$ at the two outer edges (2 unknowns fewer),\n",
    "3. impose continuity of $\\psi$ and $d\\psi/dx$ at every interface ($2N-2$ equations),\n",
    "4. set the determinant of the coefficient matrix to zero, which selects the allowed energies,\n",
    "5. normalize $\\int|\\psi|^2dx = 1$ to fix the last coefficient.\n",
    "\n",
    "A tunneling problem is different: the electron comes in from one contact and may leave through the\n",
    "other. Every energy is allowed, so step 4 disappears, and the wave extends to infinity, so step 5\n",
    "disappears too. Step 2 is replaced by an *open* boundary condition: we fix what comes in. The\n",
    "interface conditions of step 3 are unchanged, and they are all the physics there is.\n",
    "\n",
    "Klimeck draws the single barrier as a two-port network, familiar from circuit analysis: each\n",
    "interface is a box that couples a wave coming in and a wave going out on each side. A wave of\n",
    "amplitude $A$ is incident from the left, $B$ is reflected, $E$ is transmitted; $C$ and $D$ live\n",
    "inside the barrier. Usually nothing is injected from the right, $F = 0$, and the incident wave is\n",
    "normalized, $A = 1$. That removes two unknowns, and no particles are lost: what is not\n",
    "transmitted is reflected.\n",
    "\n",
    "![Slide 7: the single barrier as two scattering boxes](attachment:slide_007.png)\n",
    "\n",
    "*Slide 7: one box (matrix) per interface. A and F come in, B and E go out, C and D are the\n",
    "amplitudes inside the barrier.*"
   ],
   "attachments": {
    "slide_007.png": {
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"
    }
   }
  },
  {
   "cell_type": "markdown",
   "id": "2a5b5e5c",
   "metadata": {},
   "source": [
    "## 2. The three regions of a single barrier\n",
    "\n",
    "A barrier of height $V_0$ and width $L$ sits between $x = 0$ and $x = L$. The energy is measured\n",
    "from the conduction-band edge of the two outer regions. An electron of energy $E < V_0$ is\n",
    "classically allowed in regions 1 and 3 and forbidden in region 2. The effective-mass Schrödinger\n",
    "equation $d^2\\psi/dx^2 + k^2\\psi = 0$ has the solutions\n",
    "\n",
    "$$\\psi_1 = A e^{ikx} + B e^{-ikx}, \\qquad \\psi_2 = C e^{-\\gamma x} + D e^{\\gamma x}, \\qquad\n",
    "\\psi_3 = E e^{ikx} + F e^{-ikx},$$\n",
    "\n",
    "$$k = \\sqrt{\\frac{2mE}{\\hbar^2}}, \\qquad \\gamma = \\sqrt{\\frac{2m(V_0 - E)}{\\hbar^2}} .$$\n",
    "\n",
    "As the lecture stresses, $k$ and $\\gamma$ are the same object: each is measured from the band edge of\n",
    "its own region, upwards for $k$, downwards from the barrier top for $\\gamma$. Inside the barrier the\n",
    "wave number is imaginary, $k_2 = i\\gamma$.\n",
    "\n",
    "![Slide 9: the regions, the ansatz and the wave numbers](attachment:slide_009.png)\n",
    "\n",
    "*Slide 9: region 1 and region 3 are classically allowed, region 2 is classically forbidden.*\n",
    "\n",
    "The barrier material has its own band structure, $E = V_0 + \\hbar^2k^2/2m$. At an energy below its\n",
    "edge, its Bloch \"waves\" have a complex wave number: these are the evanescent states that the ansatz\n",
    "$e^{\\pm\\gamma x}$ describes. open-nemo's `complex_bands` computes them for the discretized barrier\n",
    "material (a chain of sites with spacing $a$); its imaginary wave number is the decay constant\n",
    "$\\gamma$. Throughout this notebook the mass is GaAs's, $m = 0.067\\,m_0$, and the barrier is\n",
    "$V_0 = 0.4$ eV high."
   ],
   "attachments": {
    "slide_009.png": {
     "image/png": 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"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4b674906",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:05.124702Z",
     "iopub.status.busy": "2026-10-25T17:49:05.124596Z",
     "iopub.status.idle": "2026-10-25T17:49:05.157127Z",
     "shell.execute_reply": "2026-10-25T17:49:05.156679Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " E (eV)   γ open-nemo (1/nm)   γ formula (1/nm)   decay length 1/γ (nm)\n",
      "  0.05           0.78453            0.78453            1.275\n",
      "  0.10           0.72633            0.72633            1.377\n",
      "  0.20           0.59305            0.59305            1.686\n",
      "  0.30           0.41935            0.41935            2.385\n",
      "  0.35           0.29652            0.29652            3.372\n"
     ]
    }
   ],
   "source": [
    "M, V0, DX = 0.067, 0.4, 0.01  # mass (m₀), barrier height (eV), grid spacing (nm)\n",
    "t0 = H2M0 / (M * DX**2)  # hopping of the discretized barrier material (eV)\n",
    "barrier_chain = nemo.Lead(np.array([[2 * t0 + V0]]), np.array([[-t0]]))\n",
    "energies = np.array([0.05, 0.1, 0.2, 0.3, 0.35])\n",
    "cb = nemo.complex_bands(barrier_chain, energies, period=DX)\n",
    "gamma_nemo = np.abs(cb[\"k_imag\"]).max(axis=1)  # 1/nm\n",
    "gamma_exact = np.sqrt(M * (V0 - energies) / H2M0)\n",
    "print(\" E (eV)   γ open-nemo (1/nm)   γ formula (1/nm)   decay length 1/γ (nm)\")\n",
    "for e, gn, ge in zip(energies, gamma_nemo, gamma_exact):\n",
    "    print(f\"{e:6.2f}   {gn:15.5f}   {ge:16.5f}   {1 / ge:14.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce1fe6d3",
   "metadata": {},
   "source": [
    "The decay constants agree to the fourth digit; the small difference is the grid ($a = 0.01$ nm): a\n",
    "discretized chain has $\\cosh(\\gamma a) = 1 + (V_0 - E)/2t_0$ rather than $\\gamma^2 = (V_0-E)/t_0a^2$.\n",
    "The decay length $1/\\gamma$ is about a nanometre: a barrier a few nanometres wide is crossed by an\n",
    "amplitude that has dropped by $e^{-\\gamma L}$, small but not zero. That is tunneling.\n",
    "\n",
    "## 3. The interface conditions as matrices\n",
    "\n",
    "At $x = 0$ continuity of $\\psi$ and $\\psi'$ gives $A + B = C + D$ and $ik(A - B) = -\\gamma(C - D)$; at\n",
    "$x = L$ the same two conditions connect $C, D$ with $E, F$. Each pair can be solved for the\n",
    "amplitudes on the left, which gives two 2×2 matrices:\n",
    "\n",
    "![Slide 11: the interface conditions and the matrices M1 and M2](attachment:slide_011.png)\n",
    "\n",
    "*Slide 11: the four interface equations, rearranged into $[A, B]^T = M_1 [C, D]^T$ and\n",
    "$[C, D]^T = M_2 [E, F]^T$.*\n",
    "\n",
    "Chaining the two, $[A, B]^T = M_1 M_2 [E, F]^T = M [E, F]^T$. With $F = 0$ the first row reads\n",
    "$A = M_{11}E$, so the transmitted amplitude is $t = E/A = 1/M_{11}$, the reflected one\n",
    "$r = B/A = M_{21}/M_{11}$, and the transmission is\n",
    "\n",
    "$$T(E) = \\left|\\frac{E}{A}\\right|^2 = \\frac{1}{|M_{11}|^2}.$$\n",
    "\n",
    "The cell below codes $M_1$ and $M_2$ exactly as printed on the slide. Above the barrier the same\n",
    "formulas hold with $\\gamma = \\sqrt{2m(V_0 - E)}/\\hbar$ imaginary, so one function covers all\n",
    "energies."
   ],
   "attachments": {
    "slide_011.png": {
     "image/png": 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"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a8702523",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:05.158286Z",
     "iopub.status.busy": "2026-10-25T17:49:05.158196Z",
     "iopub.status.idle": "2026-10-25T17:49:05.473974Z",
     "shell.execute_reply": "2026-10-25T17:49:05.473601Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "largest |R + T − 1| from the slide's matrices: 1.3e-15\n",
      "largest |ln(T open-nemo / T slide)|: 3.0e-05\n",
      "T at 2 meV = 5.3e-04, at the barrier top = 0.39\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1210x418 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def slide_matrices(E, V0, L, m=M):\n",
    "    # M1 and M2 of slide 11, for arrays of energies E (eV); L in nm\n",
    "    k = np.sqrt(m * E / H2M0 + 0j)\n",
    "    g = np.sqrt(m * (V0 - E) / H2M0 + 0j)  # imaginary above the barrier\n",
    "    M1 = 0.5 * np.array([[1 + 1j * g / k, 1 - 1j * g / k], [1 - 1j * g / k, 1 + 1j * g / k]])\n",
    "    M2 = 0.5 * np.array(\n",
    "        [\n",
    "            [(1 - 1j * k / g) * np.exp((1j * k + g) * L), (1 + 1j * k / g) * np.exp(-(1j * k - g) * L)],\n",
    "            [(1 + 1j * k / g) * np.exp((1j * k - g) * L), (1 - 1j * k / g) * np.exp(-(1j * k + g) * L)],\n",
    "        ]\n",
    "    )\n",
    "    return np.moveaxis(M1, -1, 0), np.moveaxis(M2, -1, 0)  # shape (nE, 2, 2)\n",
    "\n",
    "\n",
    "def device(layers, dx=DX):\n",
    "    # layers: (width nm, band edge eV, mass m₀); the first and the last layer are the contacts\n",
    "    mats = [\n",
    "        nemo.Layer(EM(f\"layer {j}\", m, 12.9, conduction_band_edge=v), w) for j, (w, v, m) in enumerate(layers)\n",
    "    ]\n",
    "    return nemo.Heterostructure1D(mats, spacing=dx)\n",
    "\n",
    "\n",
    "L = 3.0\n",
    "E = np.linspace(0.002, 1.0, 1500)\n",
    "M1, M2 = slide_matrices(E, V0, L)\n",
    "Mtot = M1 @ M2\n",
    "T_slide = 1 / np.abs(Mtot[:, 0, 0]) ** 2\n",
    "R_slide = np.abs(Mtot[:, 1, 0] / Mtot[:, 0, 0]) ** 2\n",
    "single = device([(5.0, 0.0, M), (L, V0, M), (5.0, 0.0, M)])\n",
    "T_nemo = nemo.Transport(single.hamiltonian).transmission(E)\n",
    "\n",
    "print(f\"largest |R + T − 1| from the slide's matrices: {np.abs(R_slide + T_slide - 1).max():.1e}\")\n",
    "print(f\"largest |ln(T open-nemo / T slide)|: {np.abs(np.log(T_nemo / T_slide)).max():.1e}\")\n",
    "print(f\"T at {E[0]*1e3:.0f} meV = {T_nemo[0]:.1e}, at the barrier top = {np.interp(V0, E, T_nemo):.2f}\")\n",
    "fig, (a1, a2) = plt.subplots(1, 2, figsize=(11, 3.8))\n",
    "a1.semilogy(E, T_slide, **style.series(\"reference\"), label=\"slide 11: 1/|M₁₁|²\")\n",
    "a1.semilogy(E, T_nemo, **style.series(lw=1.1), label=\"open-nemo (finite differences, open leads)\")\n",
    "a1.axvline(V0, color=style.CONTEXT, ls=\":\", lw=0.8)\n",
    "a1.set(xlabel=\"E (eV)\", ylabel=\"T(E)\", title=f\"one barrier, {V0} eV, {L} nm, m = {M} m₀\")\n",
    "a1.legend(frameon=False, fontsize=8)\n",
    "a2.plot(E, np.log(T_nemo / T_slide), **style.series(lw=1))\n",
    "a2.axhline(0, color=style.CONTEXT, lw=0.6)\n",
    "a2.set(xlabel=\"E (eV)\", ylabel=\"ln(T open-nemo / T slide)\", title=\"difference\")\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "032b4fdd",
   "metadata": {},
   "source": [
    "The two transmissions lie on top of each other, from $5\\cdot10^{-4}$ at 2 meV to 0.39\n",
    "at the barrier top. $T$ is far from zero below the top and, as the next lecture shows, still below one\n",
    "above it: there is no sharp classical threshold (the subject of the next lecture). The matrices conserve the current: reflection\n",
    "and transmission add up to one to round-off. The remaining difference, at most $3\\cdot10^{-5}$ in\n",
    "$\\ln T$, is the discretization of open-nemo's grid, which grows with energy because the error of\n",
    "the three-point second derivative scales as $(ka)^2$ (Lecture 6.5).\n",
    "\n",
    "## 4. The general transfer-matrix method\n",
    "\n",
    "Nothing in this construction is special to one barrier. For any stack of layers $j = 1 \\dots N$ of\n",
    "constant potential $V_j$ and mass $m_j$, write in each layer\n",
    "\n",
    "$$\\psi_j(x) = A_j^+ e^{ik_j(x - x_j)} + A_j^- e^{-ik_j(x - x_j)}, \\qquad\n",
    "k_j = \\sqrt{2m_j(E - V_j)}/\\hbar$$\n",
    "\n",
    "(real or imaginary), with $x_j$ the left edge of the layer. Continuity of $\\psi$ and of the flux\n",
    "$\\psi'/m$ (the BenDaniel–Duke condition, needed when the mass changes from layer to layer) at each\n",
    "interface gives one 2×2 matrix per interface, and\n",
    "\n",
    "$$\\begin{pmatrix}A_1^+\\\\A_1^-\\end{pmatrix} = \\prod_j M^{(j)} \\begin{pmatrix}A_N^+\\\\A_N^-\\end{pmatrix}.$$\n",
    "\n",
    "With $A_1^+ = 1$ and $A_N^- = 0$ the transmission is\n",
    "$T = \\frac{k_N/m_N}{k_1/m_1}\\,|1/M_{11}|^2$: the prefactor is the ratio of the group velocities in\n",
    "the two contacts, which is 1 when they are the same material. The function below implements this\n",
    "for many energies at once, and the first check is that it reproduces the slide's $M_1M_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d7b5eda1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:05.475059Z",
     "iopub.status.busy": "2026-10-25T17:49:05.474972Z",
     "iopub.status.idle": "2026-10-25T17:49:05.480631Z",
     "shell.execute_reply": "2026-10-25T17:49:05.480084Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "general code against the slide's M1·M2: largest |ΔM| / |M| = 5.0e-16\n"
     ]
    }
   ],
   "source": [
    "def interface_steps(layers, E):\n",
    "    # one 2×2 matrix per interface (nE, 2, 2): [A_j⁺, A_j⁻] = step_j [A_j+1⁺, A_j+1⁻]\n",
    "    E = np.atleast_1d(E).astype(complex)\n",
    "    k = [np.sqrt(m * (E - v) / H2M0 + 0j) for _, v, m in layers]\n",
    "    steps = []\n",
    "    for j in range(len(layers) - 1):\n",
    "        d = layers[j][0] if j > 0 else 0.0  # the first contact: origin at the interface\n",
    "        (mj, kj), (mn, kn) = (layers[j][2], k[j]), (layers[j + 1][2], k[j + 1])\n",
    "        ep, em = np.exp(1j * kj * d), np.exp(-1j * kj * d)\n",
    "        W = np.array([[ep, em], [1j * kj / mj * ep, -1j * kj / mj * em]])  # ψ, ψ'/m of layer j\n",
    "        Wn = np.array([[np.ones_like(kn), np.ones_like(kn)], [1j * kn / mn, -1j * kn / mn]])\n",
    "        steps.append(np.linalg.solve(np.moveaxis(W, -1, 0), np.moveaxis(Wn, -1, 0)))\n",
    "    return steps, k\n",
    "\n",
    "\n",
    "def transfer_matrix(layers, E):\n",
    "    # the product of the interface matrices, and the wave numbers k_j(E) (1/nm)\n",
    "    steps, k = interface_steps(layers, E)\n",
    "    total = steps[0]\n",
    "    for s in steps[1:]:\n",
    "        total = total @ s\n",
    "    return total, k\n",
    "\n",
    "\n",
    "def tmm_transmission(layers, E):\n",
    "    total, k = transfer_matrix(layers, E)\n",
    "    flux = (k[-1] / layers[-1][2]).real / (k[0] / layers[0][2]).real\n",
    "    return flux / np.abs(total[:, 0, 0]) ** 2\n",
    "\n",
    "\n",
    "one = [(0.0, 0.0, M), (L, V0, M), (0.0, 0.0, M)]\n",
    "total, k = transfer_matrix(one, E)\n",
    "# the slide counts the phase of E and F from x = 0, this code from x = L: E_slide = E e^(−ikL)\n",
    "phase = np.stack([np.exp(1j * k[0] * L), np.exp(-1j * k[0] * L)], axis=-1)[:, None, :]\n",
    "print(\n",
    "    f\"general code against the slide's M1·M2: largest |ΔM| / |M| = \"\n",
    "    f\"{np.abs(total * phase - Mtot).max() / np.abs(Mtot).max():.1e}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce13fc88",
   "metadata": {},
   "source": [
    "Same matrices, once the phase convention is matched: the slide counts the phase of $E$ and $F$ from\n",
    "$x = 0$, the general code from the right interface $x = L$, which multiplies $E$ by $e^{ikL}$ and\n",
    "leaves $|M_{11}|$, and $T$, unchanged. The homework the lecture suggests is the double barrier: four interfaces instead of\n",
    "two. Here it is computed both ways, together with a heterostructure in which the barrier has a\n",
    "heavier mass ($0.092\\,m_0$, as in AlGaAs) and the right contact sits 0.1 eV lower than the left\n",
    "one, so that all three ingredients of the general formula (complex $k_j$, the mass in the flux, the\n",
    "velocity ratio) are exercised."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "50e6a2f4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:05.481668Z",
     "iopub.status.busy": "2026-10-25T17:49:05.481595Z",
     "iopub.status.idle": "2026-10-25T17:49:05.778285Z",
     "shell.execute_reply": "2026-10-25T17:49:05.777850Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "double barrier 2 | 6 | 2 nm, 0.4 eV: median |ln T ratio| 2.4e-05, largest 1.6e-04\n",
      "barrier mass 0.092 m₀, right contact −0.1 eV: median |ln T ratio| 1.0e-05, largest 4.1e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1210x418 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cases = {\n",
    "    \"double barrier 2 | 6 | 2 nm, 0.4 eV\": [(5, 0, M), (2, V0, M), (6, 0, M), (2, V0, M), (5, 0, M)],\n",
    "    \"barrier mass 0.092 m₀, right contact −0.1 eV\": [(5, 0, M), (3, V0, 0.092), (5, -0.1, M)],\n",
    "}\n",
    "E2 = np.linspace(0.003, 0.8, 4000)\n",
    "fig, axes = plt.subplots(1, 2, figsize=(11, 3.8))\n",
    "for ax, (name, layers) in zip(axes, cases.items()):\n",
    "    t_tmm = tmm_transmission(layers, E2)\n",
    "    t_nemo = nemo.Transport(device(layers).hamiltonian).transmission(E2)\n",
    "    ax.semilogy(E2, t_tmm, **style.series(\"reference\"), label=\"transfer matrices\")\n",
    "    ax.semilogy(E2, t_nemo, **style.series(lw=1.0), label=\"open-nemo\")\n",
    "    ax.set(xlabel=\"E (eV)\", ylabel=\"T(E)\", title=name)\n",
    "    ax.title.set_fontsize(10)\n",
    "    print(\n",
    "        f\"{name}: median |ln T ratio| {np.median(np.abs(np.log(t_nemo / t_tmm))):.1e}, \"\n",
    "        f\"largest {np.abs(np.log(t_nemo / t_tmm)).max():.1e}\"\n",
    "    )\n",
    "axes[0].legend(frameon=False, fontsize=8)\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c527105",
   "metadata": {},
   "source": [
    "The double barrier transmits completely, $T = 1$, at an energy well below the barrier top: resonant\n",
    "tunneling, the topic of Lecture 6.3. The largest differences sit on the flanks of that sharp\n",
    "peak, where a tiny shift of the peak energy changes $T$ a lot; the median difference is\n",
    "$2\\cdot10^{-5}$. In the heterostructure, waves enter only above the left contact's edge ($E = 0$), and the\n",
    "step between the two contacts reflects part of the wave even far above the barrier, so $T$ stays\n",
    "below one there.\n",
    "\n",
    "The difference between the two methods is open-nemo's grid. Halving the spacing should divide it by\n",
    "four:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0f5a2034",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:05.779331Z",
     "iopub.status.busy": "2026-10-25T17:49:05.779259Z",
     "iopub.status.idle": "2026-10-25T17:49:05.855941Z",
     "shell.execute_reply": "2026-10-25T17:49:05.855541Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " spacing (nm)   median |ln T_nemo − ln T_TMM|\n",
      "    0.1000      3.69e-03\n",
      "    0.0500      9.21e-04\n",
      "    0.0250      2.30e-04\n",
      "    0.0125      5.75e-05\n"
     ]
    }
   ],
   "source": [
    "layers = cases[\"double barrier 2 | 6 | 2 nm, 0.4 eV\"]\n",
    "Ec = np.linspace(0.01, 0.39, 400)\n",
    "t_ref = tmm_transmission(layers, Ec)\n",
    "print(\" spacing (nm)   median |ln T_nemo − ln T_TMM|\")\n",
    "for dx in (0.1, 0.05, 0.025, 0.0125):\n",
    "    t = nemo.Transport(device(layers, dx).hamiltonian).transmission(Ec)\n",
    "    print(f\"{dx:10.4f}      {np.median(np.abs(np.log(t / t_ref))):.2e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83d03a48",
   "metadata": {},
   "source": [
    "It does: the finite-difference solution converges to the transfer-matrix one as $a^2$. For piecewise\n",
    "constant potentials the transfer matrices are exact, and they are an excellent check on any numerical\n",
    "code.\n",
    "\n",
    "## 5. The wave function from the coefficients\n",
    "\n",
    "The transfer matrix gives more than $T$: once $E = t$ is known, $[A_j^+, A_j^-]$ follows in every\n",
    "layer, and with it $\\psi(x)$. Below, the single barrier at $E = 0.2$ eV (half the barrier height).\n",
    "open-nemo returns the density injected from the left contact (`spectral_left`, the diagonal of\n",
    "$G\\Gamma_LG^\\dagger$), which is $|\\psi|^2$ of the same scattering state up to a constant; it is\n",
    "scaled here so that it equals $|t|^2$ in the right contact."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a412c67e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:05.857156Z",
     "iopub.status.busy": "2026-10-25T17:49:05.857074Z",
     "iopub.status.idle": "2026-10-25T17:49:05.859786Z",
     "shell.execute_reply": "2026-10-25T17:49:05.859476Z"
    }
   },
   "outputs": [],
   "source": [
    "def wave_function(layers, E, x):\n",
    "    # ψ(x) of the state injected from the left with A = 1; x = 0 at the first interface\n",
    "    steps, k = interface_steps(layers, [E])\n",
    "    total, _ = transfer_matrix(layers, [E])\n",
    "    coeffs = [None] * len(layers)\n",
    "    coeffs[-1] = np.array([1 / total[0, 0, 0], 0])  # last layer: E = t, F = 0\n",
    "    for j in range(len(layers) - 2, -1, -1):  # walk back to the left\n",
    "        coeffs[j] = steps[j][0] @ coeffs[j + 1]\n",
    "    edges = np.concatenate([[0.0], np.cumsum([w for w, _, _ in layers[1:-1]])])\n",
    "    origin = np.concatenate([[0.0], edges])  # where each layer's phase is counted from\n",
    "    bounds = np.concatenate([[-np.inf], edges, [np.inf]])\n",
    "    psi = np.zeros_like(x, dtype=complex)\n",
    "    for j, c in enumerate(coeffs):\n",
    "        sel = (x >= bounds[j]) & (x < bounds[j + 1])\n",
    "        psi[sel] = c[0] * np.exp(1j * k[j][0] * (x[sel] - origin[j])) + c[1] * np.exp(\n",
    "            -1j * k[j][0] * (x[sel] - origin[j])\n",
    "        )\n",
    "    return psi, coeffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "370a1083",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:05.860694Z",
     "iopub.status.busy": "2026-10-25T17:49:05.860627Z",
     "iopub.status.idle": "2026-10-25T17:49:05.995372Z",
     "shell.execute_reply": "2026-10-25T17:49:05.994970Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E = 0.2 eV: |t|² = 1.0772e-01, |r|² = 0.892276, C = 0.9723-0.9723j, D = 2.77e-02+2.77e-02j\n",
      "largest | |ψ|²(TMM) − scaled open-nemo density | = 3.5e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 990x418 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "LEAD = 5.0\n",
    "layers = [(LEAD, 0.0, M), (L, V0, M), (LEAD, 0.0, M)]\n",
    "Ew = 0.2\n",
    "dev = device(layers)\n",
    "x = dev.x - LEAD  # the barrier starts at x = 0\n",
    "psi, coeffs = wave_function(layers, Ew, x)\n",
    "res = nemo.Transport(dev.hamiltonian).solve(np.array([Ew]))\n",
    "rho = res[\"spectral_left\"][0]\n",
    "t2 = np.abs(coeffs[-1][0]) ** 2\n",
    "rho = rho * t2 / rho[x > L + 1].mean()\n",
    "print(\n",
    "    f\"E = {Ew} eV: |t|² = {t2:.4e}, |r|² = {np.abs(coeffs[0][1])**2:.6f}, C = {coeffs[1][0]:.4f}, D = \"\n",
    "    f\"{coeffs[1][1]:.2e}\"\n",
    ")\n",
    "print(f\"largest | |ψ|²(TMM) − scaled open-nemo density | = {np.abs(np.abs(psi)**2 - rho).max():.1e}\")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9, 3.8))\n",
    "ax.axvspan(0, L, color=style.CONTEXT, alpha=0.18, lw=0, label=\"barrier\")\n",
    "ax.plot(\n",
    "    x, np.abs(psi) ** 2, **style.series(\"reference\"), label=\"|ψ|² from the transfer matrices\"\n",
    ")\n",
    "ax.plot(x, rho, **style.series(lw=1.1), label=\"open-nemo injected density (scaled)\")\n",
    "ax.set(\n",
    "    xlabel=\"x (nm)\",\n",
    "    ylabel=\"|ψ(x)|² (incident amplitude 1)\",\n",
    "    yscale=\"log\",\n",
    "    ylim=(1e-3, 5),\n",
    "    title=f\"single barrier {V0} eV, {L} nm, at E = {Ew} eV\",\n",
    ")\n",
    "ax.legend(frameon=False, fontsize=8, loc=\"lower left\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "240c6177",
   "metadata": {},
   "source": [
    "On the left, the incident and reflected waves interfere: $|\\psi|^2 = |e^{ikx} + re^{-ikx}|^2$\n",
    "oscillates between $(1-|r|)^2$ and $(1+|r|)^2$, almost a standing wave because $|r|^2$ is close to\n",
    "one. Inside the barrier the density falls exponentially, mostly through $C e^{-\\gamma x}$; the\n",
    "growing term $De^{\\gamma x}$ has a tiny coefficient and only bends the curve near $x = L$, where it\n",
    "is needed to match the outgoing wave. On the right only the transmitted wave remains, with the\n",
    "constant density $|t|^2$. The two methods give the same state.\n",
    "\n",
    "## 6. Simple and pleasing, with a catch\n",
    "\n",
    "The lecture calls the method \"conceptually very simple and analytically pleasing\", and recommends it\n",
    "for the double-barrier homework, but warns that it has numerical issues. The cause is visible in\n",
    "the matrices: an evanescent layer contributes $e^{+\\gamma d}$ and $e^{-\\gamma d}$ to the same\n",
    "product. The size of $M_{11}$ grows exponentially with the barrier width, and every quantity that\n",
    "results from a cancellation between such terms keeps only the digits left over by floating-point\n",
    "arithmetic (about 16)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9645e3ff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:05.996420Z",
     "iopub.status.busy": "2026-10-25T17:49:05.996347Z",
     "iopub.status.idle": "2026-10-25T17:49:05.999286Z",
     "shell.execute_reply": "2026-10-25T17:49:05.998996Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " barrier width (nm)   γL      |M11|       T = 1/|M11|²    det M as computed (exactly 1)\n",
      "           1          0.6    1.181e+00      7.169e-01     +1.000000e+00\n",
      "           2          1.2    1.790e+00      3.122e-01     +1.000000e+00\n",
      "           5          3.0    9.726e+00      1.057e-02     +1.000000e+00\n",
      "          10          5.9    1.882e+02      2.824e-05     +1.000000e+00\n",
      "          20         11.9    7.082e+04      1.994e-10     +9.999990e-01\n",
      "          30         17.8    2.665e+07      1.408e-15     +1.125000e+00\n",
      "          40         23.7    1.003e+10      9.941e-21     +0.000000e+00\n"
     ]
    }
   ],
   "source": [
    "widths = np.array([1, 2, 5, 10, 20, 30, 40])\n",
    "print(\" barrier width (nm)   γL      |M11|       T = 1/|M11|²    det M as computed (exactly 1)\")\n",
    "for w in widths:\n",
    "    tot, _ = transfer_matrix([(0, 0, M), (w, V0, M), (0, 0, M)], [0.2])\n",
    "    m11 = np.abs(tot[0, 0, 0])\n",
    "    det = tot[0, 0, 0] * tot[0, 1, 1] - tot[0, 0, 1] * tot[0, 1, 0]\n",
    "    print(\n",
    "        f\"{w:12d}       {np.sqrt(M * (V0 - 0.2) / H2M0) * w:6.1f}   {m11:10.3e}   {1 / m11**2:12.3e}     \"\n",
    "        f\"{det.real:+.6e}\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33f46798",
   "metadata": {},
   "source": [
    "The transfer matrix between two identical contacts has determinant exactly 1 (current\n",
    "conservation), yet its elements grow like $e^{\\gamma L}$. The determinant is the difference of two\n",
    "products of size $|M_{11}|^2$: as computed, it keeps fewer and fewer correct digits as the barrier\n",
    "widens, and when $|M_{11}|^2$ approaches $10^{16}$ none are left (the last rows of the table). For a single barrier $T = 1/|M_{11}|^2$ is still accurate, because no cancellation is\n",
    "needed. For many layers, for the wave function deep inside thick barriers, or for a resonance that\n",
    "needs a large $M_{11}$ to cancel down to one, the precision is lost. Lecture 6.5 returns to this,\n",
    "and to the discretized Schrödinger equation that open-nemo solves instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9b46fc5a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-25T17:49:06.000416Z",
     "iopub.status.busy": "2026-10-25T17:49:06.000347Z",
     "iopub.status.idle": "2026-10-25T17:49:06.301018Z",
     "shell.execute_reply": "2026-10-25T17:49:06.300485Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 770x396 with 1 Axes>"
      ]
     },
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    }
   ],
   "source": [
    "# exploration: T at E = V0/2 against barrier width, transfer matrices and open-nemo\n",
    "w = np.linspace(0.5, 12, 24)\n",
    "t_tmm = [tmm_transmission([(0, 0, M), (wi, V0, M), (0, 0, M)], [V0 / 2])[0] for wi in w]\n",
    "t_nemo = [\n",
    "    nemo.Transport(device([(3, 0, M), (wi, V0, M), (3, 0, M)], dx=0.05).hamiltonian).transmission([V0 / 2])[0]\n",
    "    for wi in w\n",
    "]\n",
    "gam = np.sqrt(M * V0 / 2 / H2M0)\n",
    "fig, ax = plt.subplots(figsize=(7, 3.6))\n",
    "ax.semilogy(w, t_tmm, \"o\", color=style.REFERENCE, mfc=\"none\", ms=5, label=\"transfer matrices\")\n",
    "ax.semilogy(w, t_nemo, \"-\", color=style.OPEN_NEMO, lw=1.2, label=\"open-nemo (spacing 0.05 nm)\")\n",
    "ax.semilogy(w, np.exp(-2 * gam * w), \":\", color=style.CONTEXT, label=r\"$e^{-2\\gamma L}$\")\n",
    "ax.set(\n",
    "    xlabel=\"barrier width L (nm)\", ylabel=\"T at E = V₀/2\", title=\"tunneling falls exponentially with width\"\n",
    ")\n",
    "ax.legend(frameon=False, fontsize=8);"
   ]
  },
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   "id": "b5c51528",
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   "source": [
    "Every nanometre of barrier costs the same factor, $e^{-2\\gamma\\cdot 1\\,\\text{nm}}$, once the barrier\n",
    "is wider than about one decay length: the exponential law that Lecture 6.2 derives from the exact\n",
    "formula. The dotted line has that slope; the curves lie above it by the prefactor\n",
    "$(4k\\gamma/(k^2+\\gamma^2))^2$, which is 4 at $E = V_0/2$, where $k = \\gamma$.\n",
    "\n",
    "## Summary\n",
    "\n",
    "- An open system differs from a closed one only in its boundary conditions: the incident amplitude\n",
    "  is fixed ($A = 1$, $F = 0$), every energy is allowed, and there is no normalization.\n",
    "- In each region of constant potential the solution is $e^{\\pm ikx}$ (allowed) or $e^{\\pm\\gamma x}$\n",
    "  (forbidden, $k = i\\gamma$); $\\gamma$ is the imaginary wave number of the barrier's complex band\n",
    "  structure.\n",
    "- Continuity of $\\psi$ and $\\psi'/m$ at each interface is a 2×2 matrix; their product is the\n",
    "  transfer matrix $M$, and $T = (v_N/v_1)/|M_{11}|^2$.\n",
    "- The slide's $M_1M_2$, a general transfer-matrix code and open-nemo's finite-difference transport\n",
    "  agree; the latter converges as $a^2$ to the exact piecewise-constant result. The wave function\n",
    "  rebuilt from the coefficients is open-nemo's injected density.\n",
    "- The matrix elements grow as $e^{\\gamma L}$ while $\\det M = 1$: the method loses precision when\n",
    "  large terms must cancel.\n",
    "\n",
    "## Exercises\n",
    "\n",
    "1. Use `tmm_transmission` to compute $T(E)$ of a double barrier with 3 nm barriers and a 5 nm well,\n",
    "   and find the energy of the transmission peak. Compare with `nemo.resonances(device(...))`.\n",
    "2. Make the right contact 0.2 eV lower than the left one (a step) and remove the barrier. Check that\n",
    "   $R + T = 1$ when $T$ includes the velocity ratio, and that it fails without it.\n",
    "3. Plot $|\\psi(x)|^2$ for the single barrier at $E = 0.6$ eV, above the barrier. What replaces the\n",
    "   exponential decay inside it?\n",
    "4. Repeat the table of section 6 at $E = 0.39$ eV. Why does $M_{11}$ grow so much more slowly?\n",
    "\n",
    "## Further reading\n",
    "\n",
    "- [Quantum transport from scratch: Green's functions on a 1-D chain](../../book/04_resonant_tunneling_diodes/04_01_open_systems_and_wells/04_01_01_greens_functions_from_scratch.ipynb):\n",
    "  the open boundary conditions that open-nemo uses instead of transfer matrices.\n",
    "- [Benchmark: piecewise-constant barriers against nanoHUB's PCPBT](../../book/15_benchmarks/15_05_nanohub_tools/15_05_01_band_structures_and_barriers/15_05_01_04_pcpbt.ipynb):\n",
    "  open-nemo against the transfer-matrix tool used throughout Section 6.\n",
    "- [Resonant tunneling diode, step by step](../../book/04_resonant_tunneling_diodes/04_01_open_systems_and_wells/04_01_03_rtd_tutorial.ipynb).\n",
    "- The tool of the lecture: [Piece-Wise Constant Potential Barriers Tool (PCPBT)](https://nanohub.org/tools/pcpbt) on nanoHUB.\n",
    "- The numerical limits of transfer matrices and better methods: G. Klimeck, *Nanoelectronic\n",
    "  Modeling: From Quantum Mechanics and Atoms to Realistic Devices*,\n",
    "  [nanoHUB resource 8086](https://nanohub.org/resources/8086) (2010)."
   ]
  }
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