---
title: Surface-State-Assisted Tunneling
url: https://www.emergentmind.com/topics/surface-state-assisted-tunneling
type: topic
---

# Surface-State-Assisted Tunneling

Surface-state-assisted tunneling denotes a class of transport processes in which electronic states localized at a surface, interface, or edge materially participate in tunneling. In the current literature, that participation ranges from semiconductor–oxide interface trapping and defect-mediated injection to resonant transport through adatom-induced gap states, tunneling through Shockley or Tamm surface bands, transport through superconducting bound states and Majorana-related surface channels, and barrier reshaping by reconstructed surface-confined metallic layers. The phrase is therefore broader than any single microscopic mechanism, and several papers use more specific terms such as *interface states*, *adatom-induced gap state*, *Shockley surface state*, *Tamm-type surface state*, *Yu–Shiba–Rusinov state*, *surface Andreev bound state*, *Fermi arc state*, or *electronic reconstruction* [2601.06927], [2504.12055], [2103.11120], [2006.10329], [1502.05048], [1112.5036], [1606.08735], [1711.04622].

## 1. Terminology and phenomenological scope

A narrow usage would restrict surface-state-assisted tunneling to transport through canonical intrinsic surface bands such as Shockley or Tamm states. The recent literature does not support that restriction. In strained Ge/SiGe, the relevant assisting states are *interface states* at the semiconductor–oxide boundary rather than a buried heterointerface state [2601.06927]. In Au/WSe\(_2\), the assisting state is an *Au-adatom-induced localized in-gap state* rather than a native extended surface band [2504.12055]. In ultrathin oxides, terrace-edge conductance enhancement is attributed to *electronic reconstruction* and partial metallization of a surface layer rather than to a discrete trap or a conventional surface band [1711.04622]. In CeCoIn\(_5\), STM contrast arises from tunneling into a surface-reconstructed, correlation-enhanced \(d\)-orbital texture rather than into a named Shockley/Tamm state [1706.09753].

| Representative platform | Assisting state | Characteristic transport signature |
|---|---|---|
| Strained Ge/SiGe heterostructure | Semiconductor–oxide interface states [2601.06927] | TAT-to-Fowler–Nordheim crossover |
| Au adatom on WSe\(_2\) | Adatom-induced localized in-gap state [2504.12055] | Resonant double-barrier tunneling with vibrational sidebands |
| Au(111) | Shockley surface state [2103.11120] | Additional channel near \(E_F\); interference-induced transmission drop |
| La(0001) | Unoccupied Tamm-type surface state [2006.10329] | Stark shift and linewidth broadening in STM |
| Pb/Mn/Pb superconducting STM | Yu–Shiba–Rusinov state [1502.05048] | Single-electron to Andreev crossover |
| Na\(_3\)Bi thin film | Fermi arc surface states [1606.08735] | Finite transmission inside a bulk gap |

A second common simplification is to equate the topic only with conductance enhancement. Several systems instead show suppression or line-shape inversion once a surface-related channel interferes with a background bulk channel. The Au(111) Shockley state can generate a robust transmission drop at the surface-state band edge through coupling between bulk and surface-state transport channels, and the theoretical impurity-on-surface model produces position-dependent peak, dip, and asymmetric Fano-like structures through interference between direct and resonant tunneling paths [2103.11120], [1005.3664].

## 2. Semiconductor–oxide interfaces and trap-mediated injection

In strained Ge/SiGe quantum devices, the most explicit modern use of the topic is the cryogenic filling of interface states at the semiconductor–oxide boundary in a reverse-graded Hall-bar FET. The carrier path is from a 2D hole gas in a **16 nm strained Ge quantum well**, upward through a **32 nm Si\(_{0.2}\)Ge\(_{0.8}\)** barrier, to interface states near the top-surface semiconductor–oxide boundary, modeled as charge in the **SiO\(_x\)** region. At **\(T\approx 4.5\ \mathrm{K}\)**, each measurement cycle steps the gate to a chosen negative bias and holds it for about **\(T_{\mathrm{meas}\sim 24000\ \mathrm{s}\)**; the source-drain current then decays over time before stabilizing, consistent with gradual loss of holes from the quantum well and capture into interface states. A one-dimensional self-consistent Schrödinger–Poisson inversion reconstructs the saturated interface charge density \(p_{it}\) by matching simulated and Hall-extracted 2DHG density within 1%, and the cumulative trapped charge increases almost linearly with \(V_g\), with a Pearson correlation of **\(-0.9998\)**. The transport analysis is written as
\[
J_{\mathrm{total}}=J_{\mathrm{direct}}+J_{\mathrm{FN}}+J_{\mathrm{TAT}},
\]
with direct tunneling through the full **32 nm** barrier calculated to be negligible, around **\(10^{-30}\ \mathrm{A/m^2}\)**; the dominant mechanism is **trap-assisted tunneling (TAT)** at small and moderate negative bias, followed by a crossover to **Fowler–Nordheim tunneling** for **\(V_g \lesssim -4.0\ \mathrm{V}\)** once the barrier becomes strongly triangular [2601.06927].

That result refines a purely Fowler–Nordheim picture. The final trapped charge responsible for drift resides at the semiconductor–oxide interface, but the low-field supply path is attributed to defect states inside the SiGe barrier, likely dislocation-related. The extracted TAT current densities correspond to total leakage currents of roughly **10 pA to tens of nA** for a gate area **\(S\sim 10^{-7}\ \mathrm{m^2}\)**, matching the order of the observed current evolution, and the same two-regime picture survives sensitivity analysis of trap density, capture cross section, and trap energy [2601.06927].

The TFET literature places the same physics in a room-temperature device context. In top-gate, double-gate, and gate-all-around tunnel FETs, traps positioned in the source–channel tunneling region provide an intermediate path that precedes direct band-to-band tunneling. Within a modified Shockley–Read–Hall description, the field-enhancement factor \(\Gamma\) can reach about **\(10^8\)** for typical TFET fields of **\(1\text{–}5\times 10^{6}\ \mathrm{V/cm}\)**, so phonon-assisted interface TAT dominates the leakage before BTBT turns on and obscures the steep turn-on at room temperature for common trap densities. The same study argues that, unless BTBT can be increased separately, the interface trap density \(D_{it}\) must be reduced by roughly **40–100 times** compared with the state of the art for the steep turn-on of III–V TFETs to become clearly observable at room temperature; it further identifies the combination of the intrinsic Urbach tail and the surface trap density as the determinant of subthreshold swing [1603.06654].

## 3. Localized resonances in STM and spectroscopic line shapes

A clean realization of localized-state-assisted tunneling is provided by STM on single Au adatoms on double-layer WSe\(_2\) grown on epitaxial graphene. The transport geometry is a natural double barrier, tip–vacuum–Au state–WSe\(_2\)–graphene, and the Au adatom creates a localized in-gap state mainly derived from the unpaired Au \(6s\) orbital hybridized with surrounding TMD orbitals. Its energy lies inside the **\(\sim 1.8\ \mathrm{eV}\)** band gap near the Fermi level, but varies from adatom to adatom because of disorder potential; a survey over **88 individual adatoms** gives a distribution centered at **\(-9 \pm 5\ \mathrm{mV}\)** with **\(\sigma = 54 \pm 5\ \mathrm{mV}\)**. The junction is strongly asymmetric, with \(|V_c/V_0|=8.6\pm 0.19\) and hence **\(\alpha\approx 0.10\)**. Around the resonance \(V_0\), the conductance shows equally spaced vibrational sidebands with spacing **\(16.2 \pm 0.2\ \mathrm{mV}\)**, corresponding to **\(14.6 \pm 0.2\ \mathrm{meV}\)** after voltage-division correction, and Poisson-distributed intensities with **Huang–Rhys factor \(S = 2.81 \pm 0.05\)**. The mechanistic picture is therefore not just resonant tunneling through a surface-localized state, but *vibration-assisted resonant double-barrier tunneling* through an adatom-induced in-gap state [2504.12055].

The theoretical impurity-on-semiconductor-surface model clarifies how such localized assisting states alter STM observables even without vibrational structure. It couples a semiconductor continuum to a tip continuum through two simultaneous pathways: a direct channel and a resonant channel via a localized surface/impurity state. The local \(dI/dV(\omega,x)\) contains both \(\operatorname{Re}G^R_{dd}\) and \(\operatorname{Im}G^R_{dd}\), weighted by tunneling rates and modulated by \(\cos(2k_x(\omega)x)\), so the conductance depends not only on energy but also on lateral position. For shallow impurities, a self-consistent mean-field treatment shifts the effective level to \(\widetilde{\varepsilon}_d=\varepsilon_d+U\langle n_d\rangle\); for deep impurities, the Hubbard-I approximation produces an additional feature near \(\varepsilon_d+U\). The result is a family of peak, dip, and asymmetric line shapes that evolve over distances comparable to the lattice period and are strongly modified by on-site Coulomb interaction [1005.3664].

These two cases establish a general point. A surface-localized assisting state need not merely add a resonance to the local density of states. It can define the voltage-division physics of a double-barrier junction, produce charging peaks and vibronic sidebands, or act as one arm of an interference problem in which the measured conductance is a coherent superposition of direct and resonant channels [2504.12055], [1005.3664].

## 4. Intrinsic surface bands, interference, and junction-field renormalization

Canonical intrinsic surface bands remain an important limiting case. On La(0001), tunneling spectroscopy resolves an unoccupied **Tamm-type surface state** of \(d\)-band origin at **\(E_0 = 106\ \mathrm{meV}\)** above \(E_F\) in the low-current limit. Varying the tunneling current from **0.1 nA to 8000 nA** at **1.7 K** changes the local junction field while the current–distance relation remains exponential over **7.3 Å**, so the system stays in the tunneling regime. Under these conditions the resonance shifts by **45.9 meV** toward lower energy, corresponding to **43.3%** of the initial peak position, and its linewidth broadens with a slope **\(|dI/dE_0| = 2.14\)**. The state therefore acts as a field-renormalized resonant final state: the surface channel remains the same object spectroscopically, but its energy and lifetime are strongly modified by the tip-vacuum-sample field [2006.10329].

On Au(111), the relevant intrinsic state is the Shockley surface state in the projected bulk gap. In a semi-infinite surface calculation its binding energy at \(\Gamma\) is about **\(0.4\,\mathrm{eV}\)** below the Fermi level and it is mainly of \(p\)-orbital character. When a tip tunnels into a clean Au(111) surface, this state opens an additional transport channel above its band edge; near the Fermi energy it can contribute **more than 30\%** of the electron transport. Once the junction becomes more strongly coupled, however, the same surface channel can suppress transmission through destructive quantum interference between bulk and surface-state transport paths, producing a significant and robust transmission drop at the surface-state band edge in both metallic and molecular junctions. Capturing this physics requires a real-space self-energy construction that retains surface-propagating asymptotic states; standard supercell NEGF with periodic in-plane boundary conditions misses that contribution [2103.11120].

Taken together, these systems show that intrinsic surface bands are not passive spectroscopic markers. They can act as additional channels, as field-sensitive resonances, or as interference pathways that reshape transmission. The sign of the effect—enhancement or suppression—is therefore not universal [2006.10329], [2103.11120].

## 5. Superconducting and topological boundary channels

In superconductors, surface-state-assisted tunneling appears most clearly through impurity-induced and topological bound states inside the gap. For a Pb-coated superconducting tip tunneling into a Pb(111) substrate with a Mn adatom, the assisting state is a localized Yu–Shiba–Rusinov state at energy \(\epsilon_0\). With weak tip coupling, the dominant current is single-electron tunneling into the Shiba state, followed by relaxation between the bound state and the quasiparticle continuum; with stronger coupling, resonant Andreev reflection through the same state dominates. The main thresholds occur at \(eV=\pm(\Delta+\epsilon_0)\), while thermal peaks appear at \(eV=\pm(\Delta-\epsilon_0)\). This system demonstrates that a localized surface or near-surface subgap state can mediate both sequential single-particle transport and coherent two-electron transfer, with the crossover determined by the competition between tunnel rates and relaxation rates [1502.05048].

Microwave irradiation exposes the same distinction at the level of photon-assisted sidebands. For a superconducting STM junction irradiated at **\(f=40\,\mathrm{GHz}\)**, the generalized Tien–Gordon form
\[
G(V)=\sum_n J_n^2\!\left(\frac{k eV_{\mathrm{HF}}}{\hbar\Omega}\right) G^{(0)}\!\left(V+\frac{n\hbar\Omega}{k e}\right)
\]
describes single-electron tunneling and ordinary \(2e\) processes into the bare substrate, but it breaks down for tunneling via YSR states in the resonant Andreev regime. For a YSR state at **\(\epsilon_0 = 0.25\,\mathrm{meV}\)**, low-conductance data follow sequential single-electron sideband splitting, whereas high-conductance data exhibit a Y-shaped microwave map because the electron and hole tunneling components are dressed separately. The dominant sideband spacing remains \(\hbar\Omega/e\), even though the underlying transport is Andreev-mediated two-electron transfer [2001.09534].

Topological superconductors provide a more delocalized version of the same idea. In superconducting topological insulators, odd-parity pairing supports surface Andreev bound states realized as helical Majorana fermions. Their dispersion undergoes a structural transition—**cone \(\leftrightarrow\) caldera** in the full-gap case and **ridge \(\leftrightarrow\) valley** in the nodal case—controlled by the chemical potential and the effective mass parameter \(m_1\). Near these transitions the surface spectral weight accumulates near zero energy, and normal-metal/STI junctions develop robust zero-bias conductance peaks. The low-bias conductance is therefore not set by a generic 3D topological-superconductor surface cone alone, but by a surface-state reconstruction tied to the topological-insulator parent band structure [1112.5036].

A non-superconducting topological analog appears in Na\(_3\)Bi thin films. Confinement opens a bulk subband gap of roughly **63–79 meV**, but Fermi-arc-derived surface states remain inside that gap. In a gated three-segment thin-film device, those arc states allow finite transmission even when ordinary propagating bulk states are absent in the central segment. The finite in-gap transmission is smaller than bulk-to-bulk transmission because of poor spatial overlap between bulk source states and central surface states, but it is distinctly nonzero and absent from single-Weyl-node models that omit both intervalley scattering and Fermi arcs [1606.08735].

## 6. Reconstructed surfaces, terrace edges, and material engineering

Surface-state-assisted tunneling can also emerge from self-consistent reconstruction of the surface electronic structure. In ultrathin **BaTiO\(_3\)/SrRuO\(_3\)/SrTiO\(_3\)(001)** heterostructures, conductive AFM reveals highly conductive stripe-like regions near one-unit-cell terrace edges. For **3 u.c. BTO**, the ratio \(I_{\text{peak}}/I_{\text{background}}\) reaches about **3.0**, and spatially resolved \(I\)–\(V\) maps define a terrace-edge region on the upper terrace roughly **40 nm** wide. The current remains tunneling-like rather than ohmic, and transport fits are explained by a reduced effective tunnel-barrier width: in the terrace-plateau region **\(t_B = 1.20\) nm** and \(\phi_B = 0.375\) eV, whereas at the terrace edge **\(t_B = 0.98\) nm** and \(\phi_B = 0.370\) eV. First-principles analysis attributes this to terrace-edge-induced electronic reconstruction on a TiO\(_2\)-terminated surface, with electron-rich Ti \(3d\) states near \(E_F\) and partial metallization of the top surface layer. Termination control in ultrathin STO supports the same conclusion: the effect is present for TiO\(_2\)-terminated STO and strongly suppressed for SrO-terminated STO [1711.04622].

A conceptually related but electronically distinct case is the Co-terminated surface of CeCoIn\(_5\)(001). At **\(V_s = 10\) mV**, increasing the set current from **1 nA** to **30 nA** and then **100 nA** transforms round Co protrusions into dumbbells that alternate along **[100]** and **[010]**. Slab GGA+\(U\) calculations attribute the pattern to a surface-enhanced staggered \(d_{xz}\)-\(d_{yz}\) orbital order triggered by reduced screening and enhanced on-site Coulomb interaction at the surface. Bulk Co shows little spin polarization, **\(0.11\,\mu_B\)**, whereas surface Co reaches **\(2.00\,\mu_B\)**; the \(d_{xz}\) orbital becomes almost fully occupied while the \(d_{yz}\) orbital is half-filled, with the pattern reversed on neighboring Co sites. The tunneling lesson is that short-distance STM can become selectively sensitive to anisotropic surface-reconstructed \(d\)-orbital tails, so the topography encodes orbital order rather than merely atomic positions [1706.09753].

Across these reconstructed systems, the assisting state is neither a pre-existing trap nor a simple bulk continuation. It is created or strongly reshaped by the surface itself. A plausible implication is that surface-state-assisted tunneling should often be interpreted together with surface termination, crystalline quality, local coordination, and matrix-element selectivity rather than only with the existence of a nominal surface band.

The literature also makes clear that microscopic assignment is often model-dependent. In Ge/SiGe, the interface charge is reconstructed by an inverse Schrödinger–Poisson procedure and the TAT current uses phenomenological trap distributions and WKB coefficients; the argument for TAT-assisted filling is strong, but the participating defect species are not uniquely identified [2601.06927]. In Au(111) transport, conventional periodic in-plane NEGF can miss nonperiodic surface channels entirely, so the apparent absence of surface-state assistance may reflect the embedding scheme rather than the material [2103.11120]. Surface-state-assisted tunneling is therefore best treated as a transport category defined by the active participation of surface or interface electronic structure, not as a single universal mechanism.

Source: https://www.emergentmind.com/topics/surface-state-assisted-tunneling