Parasitic conduction channels in topological insulator thin films

Bert Voigtl\"ander; Felix L\"upke; F. Stefan Tautz; Sven Just; Vasily Cherepanov

REVIEW 4 major objections 4 minor 78 references

Parasitic conduction channels in topological insulator thin films

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper shows that the interior charge carrier density of a thin topological insulator film can be estimated from surface measurements alone, without knowing its dopant concentration.

desk verdict A practically useful band-bending recipe for TI thin-film transport, but the central dopant-independence claim is only marginally in its stated regime and the outputs are sensitive to inputs taken from the authors' own earlier analysis. read the letter →

arxiv 1908.09412 v2 pith:EXUW7B6V submitted 2019-08-26 cond-mat.mes-hall cond-mat.other

Sven Just , Felix Lüpke , Vasily Cherepanov , F. Stefan Tautz , Bert Voigtländer This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.other

keywords topologicalinsulatorthinfilmbandbendingsurfacestatesparasiticconductionchannelschargecarrierdensityARPESfour-pointtransport

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Thin films of topological insulators conduct current through several parallel channels: the protected surface states, the film interior, the interface layer, and the substrate. The interior contribution is hard to measure directly, so the authors calculate it from surface-sensitive data. Their central result is that, in the thin-film limit, the near-surface band bending is largely independent of the unknown dopant concentration inside the film, because the screening length is much longer than the film thickness. This makes it possible to estimate the total mobile charge carrier density, and hence the conductivity of the film interior, from ARPES measurements of the surface Fermi level, optionally combined with gate-dependent four-point transport. For BiSbTe$_3$, the symmetric calculation gives roughly $6\times 10^{11}$ cm$^{-2}$ and the asymmetric, gate-informed calculation gives roughly $2\times 10^{11}$ cm$^{-2}$ at zero gate voltage.

What carries the argument

The central mechanism is the comparison between the Debye screening length $L=\sqrt{\epsilon_0\epsilon_r k_B T/(q^2(n_b+p_b))}$ and the film thickness $d$. When $d\ll L$, Poisson's equation produces only weak band bending, so the boundary conditions at the top and bottom surfaces, represented by the surface Fermi levels $E_F^{\rm top}$ and $E_F^{\rm bottom}$, control the carrier distribution in the film rather than the unknown dopant concentration. Around this screening argument, the paper builds a semi-classical Poisson-Schrödinger calculation: it solves Poisson's equation with charge neutrality between the topological surface states and the space-charge layer, renormalizes the effective densities of states using quantized subbands in a square or triangular well, and iterates once to a second Poisson solution. A separate but supporting element is the charge-neutrality-level picture of the surface, which explains how trivial defect states shift the effective filling level of the Dirac cone and hence the measured surface Fermi energy.

What would settle it

Grow thin TI films of the same material with intentionally varied dopant levels, for example by changing growth stoichiometry, while keeping the surface Fermi level fixed, and measure the interior sheet carrier density at zero gate voltage; if that density shifts by more than the calculation's predicted variation across the band gap, the screening-length assumption is violated and the dopant-independent estimate fails.

Watch

Extended reading notes

Core claim

The paper establishes that in a thin topological insulator film, the top and bottom topological surface states exchange charge with the film interior until charge neutrality is reached, and because the Debye screening length $L$ far exceeds the film thickness $d$, the bands bend only weakly. As a result, a wide range of unintentional dopant concentrations leaves the band positions essentially fixed by the surface Fermi levels rather than by the bulk dopant density. The authors solve Poisson's equation for the band bending using symmetric boundary conditions (top and bottom surface Fermi levels equal) or asymmetric boundary conditions (top level from ARPES, bottom level extracted from gate-dependent four-point measurements), and they include confinement quantization through a square-well or triangular-well approximation of the band-bending potential. The integrated mobile carrier density $n_{\rm film}$ is then nearly flat as a function of the bulk Fermi energy across the band gap. For a 10 nm BiSbTe$_3$ film they obtain $n_{\rm film}\approx 6\times 10^{11}$ cm$^{-2}$ in the symmetric approximation and $\approx 2\times 10^{11}$ cm$^{-2}$ in the asymmetric approximation at zero gate voltage, with the latter being the more precise estimate. Combined with an interface conductivity measured on the bare substrate reconstruction before film growth, this allows the total measured 2D conductivity to be decomposed into surface-state, interior, interface, and substrate contributions.

Load-bearing premise

The calculation stands on the assumption that the film is much thinner than the screening length of its mobile charges, so band bending stays weak; if a material screens more efficiently, through a smaller dielectric constant, higher carrier density, or degenerate doping, the unknown dopant concentration would control the result.

Editorial extensions

If this is right

Given an ARPES measurement of the top surface Fermi level, the interior mobile carrier density of a thin TI film can be estimated without knowing its unintentional dopant concentration.
With additional gate-dependent four-point transport data, the asymmetric calculation gives a more precise value; for BiSbTe$_3$ at zero gate voltage this is about $2\times 10^{11}$ cm$^{-2}$, one third of the symmetric estimate.
Because the interface conductivity can be measured on the bare substrate reconstruction before film growth, the total measured 2D conductivity can be decomposed into TSS, interior, interface, and substrate channels.
The approach is presented as general across TI material classes, and the same gate-dependent measurements also yield the carrier mobility, so the interior conductivity itself becomes accessible.
For device design, the results imply that low-conductivity substrate terminations such as Te/Si(111)-(1$\times$1) keep parasitic interface currents negligible, whereas Bi/Si(111)-(√3$\times$√3) would carry a substantial fraction of the current.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct test of the claim would be to grow films with deliberately varied dopant concentrations and check that the interior sheet density stays on the flat plateau of the calculation's Fig. 5, rather than tracking the dopant level.
The screening-length criterion $L\gg d$ offers a quick screening rule for other TI candidates: compute $L$ from the dielectric constant and intrinsic carrier density before investing in the full ARPES-plus-gate measurement program.
Low-temperature transport, where the film interior mobility rises relative to the surface channels, would provide a sharper falsifier, because the calculated interior conductivity could be compared with measured four-point data at temperatures where the mobility difference separates the channels.
The same logic could be extended to estimate the interior carrier density of other van-der-Waals thin films with large dielectric constants, not only topological insulators, as long as the weak-bending condition is met.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper is worth a look if you work on transport in TI thin films. It offers a practical recipe: from an ARPES-measured top Fermi level and, in the asymmetric version, a bottom Fermi level extracted from gate-dependent four-probe data, you solve Poisson–Boltzmann with quantization corrections and get the mobile carrier density in the film interior. That fills a real need, because the film interior is otherwise hard to access experimentally. The extension beyond the Schottky approximation (refs 29,30) to weak bending, accumulation, and asymmetric boundary conditions is a genuine step forward. The interface conductivity measurements in Appendix A are also useful and concrete.

The paper is honest about its approximations: Boltzmann vs Fermi–Dirac can deviate by up to 50% (they note the bending is overestimated), the self-consistency loop is truncated after one and a half iterations, and the wave functions are neglected in the quantum corrections. That transparency is good.

The soft spots are real, though. The central claim — that the film carrier density is nearly independent of dopant concentration — rests on d << L. For their own BiSbTe3 parameters, L is about 20 nm, only twice the 10 nm film. That is not deep in the claimed regime, and the paper gives no measurement of epsilon_r or doping for the actual film. It says "not too high dopant levels" but doesn't say where the boundary is. Second, the asymmetric result depends on E_bottom^F and the mobility, both imported from the authors' earlier quantum-capacitance analysis (ref 21) without independent validation. Fig 8 shows n_film can change by an order of magnitude across the plausible range of E_bottom^F, and the symmetric vs asymmetric numbers differ by a factor of three. That is a wide spread for something called "well-founded." Also, Table II lists v_Fermi = 5.6e-5 m/s, which looks like a units typo (surely 5.6e5 m/s?).

The math itself is standard semiconductor physics and seems internally consistent. The paper would be stronger with error bars on n_film, a quantitative statement of the d/L regime, and a comparison against an independent measurement or another group's data.

Verdict: this deserves a serious referee. It is a useful modeling tool for a real experimental problem, with real data behind it, and the approximations are disclosed. I'd send it out, but I'd expect the reviewers to push for a sharper statement of the validity regime and for uncertainty propagation.

Referee Report

4 major / 4 minor

Summary. The manuscript proposes a semi-classical calculation of the band bending and mobile carrier density in the interior of thin topological-insulator films, using experimentally determined surface and interface Fermi levels as input. The authors solve Poisson's equation with Boltzmann statistics and a Debye screening length, treat symmetric (E_top^F = E_bottom^F) and asymmetric boundary conditions, add quantization via square or triangular infinite wells, and apply the model to a 10 nm BiSbTe3 film using parameters from earlier ARPES and gate-dependent four-probe measurements. The central claim is that in the thin-film limit d << L the band bending and integrated film carrier density n_film are nearly independent of the unknown dopant concentration (represented by E_bulk^F), so that n_film, and with a known mobility the film conductivity, can be estimated from surface-sensitive measurements alone. For the BiSbTe3 example, the symmetric approximation gives n_film ~ 6e11 cm^-2 and the asymmetric approximation ~2e11 cm^-2 at zero gate voltage.

Significance. If the central claim holds, the paper offers a practically useful way to quantify the parasitic film-interior conduction channel that otherwise contaminates transport studies of topological surface states. The analytic Poisson-band-bending framework, the explicit distinction between dopant concentration and mobile carrier density, and the use of ARPES and gate-dependent transport data as inputs are valuable strengths, and the authors are unusually explicit about their approximations. However, the quantitative usefulness of the results is conditional on assumptions that are acknowledged but not fully validated: the d << L screening regime for the specific film, the Boltzmann approximation at a Fermi level only 20 meV below the conduction band, and the reliability of E_bottom^F and the mobility imported from the earlier transport analysis. Because these assumptions directly affect the quoted numbers, the paper is more convincing as a methodological proposal than as a validated quantitative estimate.

major comments (4)

[II.B.4, Eq. (3)] The central dopant-independence claim requires d << L, but for the paper's own BiSbTe3 parameters the condition is only marginal: with epsilon_r ≈ 100 and n_b + p_b = 4e17 cm^-3, Eq. (3) gives L ≈ 19 nm, only about twice the d = 10 nm film; a factor-two reduction in epsilon_r or a tenfold increase in doping makes L ≤ d. The paper provides no measured epsilon_r or n_b + p_b for the MBE film under consideration, so the regime in which Figs. 4 and 5 are claimed to be dopant-independent is asserted rather than demonstrated. Please quantify d/L over the plausible doping range and either restrict the claim to that range or provide direct evidence that the 10 nm BiSbTe3 film is in the d << L regime.
[II.C, Fig. 8] The asymmetric result depends strongly on E_bottom^F, which is imported from the quantum-capacitance transport analysis of ref. [21]. For fixed E_top^F = 240 meV, n_film varies by up to an order of magnitude with E_bottom^F across the plotted range, and the symmetric and asymmetric values (6e11 vs 2e11 cm^-2) differ by a factor of three. If the ref. [21] analysis already determines the film channel's carrier density or conductivity, the asymmetric calculation is not an independent estimate; if it does not, the uncertainty in E_bottom^F should be propagated into n_film. Please state explicitly what ref. [21] provides and give an uncertainty budget for the quoted n_film values.
[II.B.5] The Boltzmann approximation is knowingly used outside its validity for the example: E_top^F = 240 meV lies only 20 meV below the conduction-band edge, and the text concedes deviations of up to 50% from the Fermi-Dirac distribution. Since all quantitative values, including the factor 2 to 2.5 reduction from quantization and the final n_film estimates, are derived within this scheme, the paper should show at least one representative Fermi-Dirac calculation to demonstrate that the dopant-independence conclusion and the quoted n_film values survive.
[II.B.2 and Supplemental Material B] The Schrödinger-Poisson self-consistency is truncated after one and a half iterations and wavefunction weighting is neglected. The authors state that these approximations may overestimate band bending near the surfaces and that quantization reduces n_film by a factor of 2 to 2.5 relative to the purely classical result. Because that factor materially changes the final estimates, a benchmark against a fully self-consistent solution for at least one parameter set is needed to establish the numerical accuracy of the method.

minor comments (4)

[Table II] The value v_Fermi = 5.6 × 10^-5 ms^-1 appears to be a units typo; the Dirac velocity in a topological insulator should be several orders of magnitude larger, likely 5.6 × 10^5 m/s.
[II.C and Fig. 6] The text says E_bottom^F = 156 meV at zero gate voltage while the Fig. 6 caption gives 155 meV; please make these values consistent.
[Eq. (7)] The typeset equation contains garbled square-root and brace symbols and should be checked carefully in production.
[II.B.7] The distinction between dopant concentration and mobile carrier density is helpful and should be kept; consider stating the definition of the 'bulk Fermi energy of a corresponding extended crystal' more prominently at first use.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the band-bending calculation is a genuine Poisson-equation solution with measured surface Fermi levels as boundary conditions, and the claimed dopant independence is an output, not an input.

full rationale

The paper's derivation chain is: (i) solve Poisson's equation (Eqs. 1-4) with the measured top Fermi level E_top^F from ARPES as a boundary condition; (ii) re-solve with quantized densities of states; (iii) integrate Eq. (8) to obtain the mobile carrier density n_film. The dopant independence of n_film is an output of this calculation (Figs. 4, 5, 7), not an input: E_bulk^F appears explicitly as a parameter in Eq. (8), and the calculation shows that n_film varies little with it in the d << L regime. E_top^F is an independently measured ARPES value from ref. [21]; E_bottom^F in the asymmetric branch is likewise an experimentally extracted input obtained from gate-dependent transport via quantum capacitance effects, and it is not the predicted quantity n_film. No equation in the paper defines n_film in terms of either surface Fermi level in a way that would make Eq. (8) an identity; Eq. (8) is a genuine integral over the calculated band profile. The reliance on ref. [21] for material parameters (m*, v_F, E_top^F, E_bottom^F, mobility) is self-citation, but those parameters are experimental inputs and are not derived from the quantity this paper claims to predict. The d << L regime is asserted for BiSbTe3 on the basis of a literature dielectric constant and assumed non-degenerate doping; if the regime fails, the dopant-independence claim would be incorrect, but that is a correctness or assumption risk, not circularity. The factor-of-three difference between symmetric and asymmetric results likewise indicates sensitivity to input assumptions, not that the output was fed back in. Since no specific reduction of the predicted quantity to its inputs could be quoted, no circular step is established.

Assumptions & free parameters 3 free parameters · 7 assumptions · 1 invented entities

The central claim rests on standard semiconductor band-bending theory plus domain assumptions about no pinning, long screening length, non-degenerate doping, and truncated self-consistency. Experimental inputs, including E_bottom^F and mobility, come from the authors' own earlier work (refs [12,21]). The only new experimental datum is the Te/Si(111)-(7x7) surface conductivity in Appendix A. No code or data files are provided.

free parameters (3)

E_bottom^F (bottom surface Fermi level at the interface) = 50 meV, 155 meV, 220 meV for gate voltages -30 V, 0 V, +30 V
Extracted from gate-dependent four-probe transport in ref [21]; used as the bottom boundary condition in the asymmetric band-bending calculation (Fig. 6).
E_bulk^F (bulk Fermi level representing the unknown dopant concentration) = 35-225 meV in example calculations; 130 meV (intrinsic) in asymmetric estimates
The concentration of unintentional dopants is unknown; the paper varies E_bulk^F across p-type, intrinsic, and n-type cases to demonstrate the claimed independence, and fixes it to the intrinsic value for the asymmetric gate-dependent results.
Charge carrier mobility in the TI film = below 2 cm^2/Vs at room temperature for BiSbTe3
Taken from ref [21] and related literature; used to convert the calculated carrier density into a film conductivity. It is not measured in this paper.

assumptions (7)

standard math Poisson's equation and the standard semiconductor band-bending formalism apply to TI thin films.
Section II.A.1 follows refs [17,19] in writing the Poisson-Boltzmann equation for the space-charge region.
domain assumption The topological surface states do not pin the Fermi level, so E_top^F is a free boundary set by charge transfer between the TSS and the film.
Section II.A.2 argues the Dirac-cone DOS is small; this is the basis for treating the surface Fermi level as an ARPES-measurable input rather than a pinned value.
domain assumption In the symmetric approximation, the bottom TSS has the same filling level as the top TSS (E_top^F = E_bottom^F).
Section II.B.1 introduces this as a first approximation because the bottom surface is not directly accessible.
domain assumption The Debye screening length is much larger than the film thickness for the relevant dopant range, so band bending is weak and nearly dopant-independent.
Section II.B.4 'Screening' relies on large epsilon_r (~100 for BiSbTe3, refs [13-15]) and non-degenerate doping; the central method fails if this condition is violated.
ad hoc to paper The Poisson-Schrodinger cycle can be truncated after one and a half iterations, and quantization can be represented by square or triangular wells with infinite barriers, neglecting wavefunction weighting.
Sections II.B.2 and Supplemental B state that a full self-consistent solution is not performed; the paper argues weak curvature and large work functions justify the approximation.
domain assumption The Boltzmann distribution adequately describes mobile carriers even when E_top^F is only 20 meV below the conduction band edge.
Section II.B.5 admits the Boltzmann deviation can be up to 50% in this case, but argues the resulting band bending is overestimated, so the true bending would be even smaller.
domain assumption The surface conductivity of the bare substrate reconstruction equals the interface conductivity beneath the TI film.
Appendix A justifies this by weak van der Waals coupling and the sharp interface observed in TEM [12]; it is load-bearing for the interface-channel decomposition.

invented entities (1)

Surface charge neutrality level (CNL) of the combined TSS/defect-state system
purpose: Conceptual reference level from which charge transfer between the TI surface and the film interior is computed before equilibration.
The paper states in Section II.A.4 that the CNL is 'not a quantity that can be measured'; it is a bookkeeping construct used to explain band bending, while the actual calculations substitute measured E_top^F.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Parasitic conduction channels in topological insulator thin films." pith.science (2026). https://pith.science/paper/EXUW7B6V

@misc{pith2026190809412,
  author       = {Pith},
  title        = {Pith review of: Parasitic conduction channels in topological insulator thin films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EXUW7B6V}},
  note         = {Machine review of arXiv:1908.09412}
}

read the original abstract

Thin films of topological insulators (TI) usually exhibit multiple parallel conduction channels for the transport of electrical current. Beside the topologically protected surface states (TSS), parallel channels may exist, namely the interior of the not-ideally insulating TI film, the interface layer to the substrate, and the substrate itself. To be able to take advantage of the auspicious transport properties of the TSS, the influence of the parasitic parallel channels on the total current transport has to be minimized. Because the conductivity of the interior (bulk) of the thin TI film is difficult to access by measurements, we propose here an approach for calculating the mobile charge carrier concentration in the TI film. To this end, we calculate the near-surface band bending using parameters obtained experimentally from surface-sensitive measurements, namely (gate-dependent) four-point resistance measurements and angle-resolved photoelectron spectroscopy (ARPES). While in most cases another parameter in the calculations, i.e. the concentration of unintentional dopants inside the thin TI film, is unknown, it turns out that in the thin-film limit the band bending is largely independent of the dopant concentration in the film. Thus, a well-founded estimate of the total mobile charge carrier concentration and the conductivity of the interior of the thin TI film proves possible. Since the interface and substrate conductivities can be measured by a four-probe conductance measurement prior to the deposition of the TI film, the total contribution of all parasitic channels, and therefore also the contribution of the vitally important TSS, can be determined reliably.

Figures

Figures reproduced from arXiv: 1908.09412 by the authors.

**Figure 2.** FIG. 2. (Color online) Principle of the formation of the CNL level of the TI surface for the presence of additional charged [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. (Color online) Principle of band bending in extended TI bulk crystals for three different bulk dopant concentrations, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: FIG. 4. (Color online) Calculated band diagrams using the symmetric approximation for a 10 nm BiSbTe [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. (Color online) Integrated total mobile charge car [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: FIG. 6. (Color online) Gate-dependent band-bending for a 10 nm thin BiSbTe [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 7.** Figure 7: FIG. 7. (Color online) (a) Calculated total mobile charge carrier density [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

**Figure 8.** Figure 8: FIG. 8. (Color online) Color plot of the mobile charge carrier [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9. (Color online) Measured four-point resistance of [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

**Figure 10.** Figure 10: FIG. 10. (Color online) Three different cases A - C for the asymmetric potential [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

**Figure 1.** Figure 1: FIG. 1. (Color online) Calculated band bending for a 10 nm thin film (red) and equivalent bulk crystal (blue) of the TI BiSbTe [PITH_FULL_IMAGE:figures/full_fig_p019_1.png]

**Figure 2.** Figure 2: FIG. 2. (Color online) Calculated band bending for a 10 nm thin film (red) and equivalent bulk crystal (blue) of the TI BiSbTe [PITH_FULL_IMAGE:figures/full_fig_p020_2.png]

**Figure 3.** Figure 3: FIG. 3. (Color online) Integrated mobile charge carrier densities for (a) electrons and (b) holes in a thin TI film as function of [PITH_FULL_IMAGE:figures/full_fig_p025_3.png]

**Figure 4.** Figure 4: FIG. 4. (Color online) Color plot of the integrated mobile charge carrier densities for (a) electrons and (b) holes in a thin TI [PITH_FULL_IMAGE:figures/full_fig_p026_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

78 extracted references · 77 canonical work pages

[21]

Zhang, C.-X

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Nature Physics 5, 438 (2009)

work page 2009
[1]

It can be prepared at room temperature by depositing Te on top of a re- constructed Si(111)-(7×7) surface

Te/Si(111)-(7 ×7) For Te-based van-der-Waals epitaxy, a plausible inter- face reconstruction is the Te/Si(111)-(7 ×7) reconstruc- tion, which has been reported as a template for the growth of TI ﬁlms on Si(111) [42]. It can be prepared at room temperature by depositing Te on top of a re- constructed Si(111)-(7×7) surface. In a ﬁrst step, the (7×7)-reconst...

work page
[2]

E F t op = 20 meVE F t op = 47.5 meVE F t op = 240 meVE F t op = 212.5 meVE F t op = 185 meVE F t op = 157.5 meVE F t op = 130 meVE F t op = 102.5 meVE F t op = 75 meV Majority carriers: electrons Majority carriers: holes1 01 8n b ulk ( c m-

work page
[3]

pb ulk ( c m- 3) FIG. 5. (Color online) Integrated total mobile charge car- rier density nﬁlm based on the symmetric approximation for a thin TI ﬁlm as function of the dopant concentration rep- resented by the bulk Fermi energy Ebulk F . The surface Fermi energy Etop F is an additional parameter. For Ebulk F inside the band-gap, the calculated ﬁlm carrier...

work page
[4]

This is immediately obvious from Eq

Screening The weak band bending in the thin TI ﬁlm is linked to the long screening length L compared to the small ﬁlm thickness d. This is immediately obvious from Eq. (2), which shows that the curvature of the band bending potential v is inversely proportional to the square of L. A small curvature of course also limits the value of v that can be reached ...

work page
[5]

4, only non-degenerate doping levels in the TI have been considered, all of which apparently lead to a downward band bending

Degenerate doping In Fig. 4, only non-degenerate doping levels in the TI have been considered, all of which apparently lead to a downward band bending. Of course, it is in principle also possible that the dopant concentration is suﬃciently high for the TI material to be degenerately n-doped, with Ebulk F above the conduction band edge. According to our ca...

work page
[6]

BiSbTe 3, which was studied extensively in ref

The example of BiSbTe 3 Here, we focus on the speciﬁc TI material (Bi1−xSbx)2Te3 with x = 0 .5, i.e. BiSbTe 3, which was studied extensively in ref. [21, 31]. Fig. 4 that we used above to illustrate generic properties of band bending in thin TI ﬁlms, was already calculated for this case. The assumption of a ﬁxed Etop F in Fig. 4 (a) to (c) corresponds to ...

work page
[7]

Mobile charge carrier density Within the Boltzmann approximation, the mobile charge carrier density can be calculated from the po- tential v(z) by ne(z) = nb exp[v(z)] and ph(z) = pb exp[−v(z)] for electrons and holes, respectively. In- tegrating the sum of ne(z) and ph(z) over the thickness d of the thin ﬁlm results in the total mobile charge carrier den...

work page

Show all 78 references

[8]

E F b ulk (meV) FIG. 7. (Color online) (a) Calculated total mobile charge carrier densitynﬁlm inside a 10 nm thin BiSbTe3 ﬁlm as function of the applied gate voltage (solid green line). The calculation is based on asymmetric boundary conditions for a thin ﬁlm with intrinsic do...

2004
[9]

In fact, this reconstruction forms the most common tem- plate for Te-based van-der-Waals epitaxy

Te/Si(111)-(1 ×1) A further plausible interface termination for Te-based van-der-Waals epitaxy is the Te/Si(111)-(1×1) surface. In fact, this reconstruction forms the most common tem- plate for Te-based van-der-Waals epitaxy. For exam- ple, it has been used for the growth of B...
[10]

Bi/Si(111)-( √ 3× √ 3) For Bi-based van-der-Waals epitaxy of TI ﬁlms, a com- mon growth template is the Bi/Si(111)-( √ 3× √
[11]

The conductivity of this surface reconstruc- tion is reported to beσBi√ 3× √ 3 = (1.4±0.1)×10−4 S/□ [6]

sur- face reconstruction with one monolayer Bi coverage (also named β-phase), which remains stable under Te ﬂux [42, 45–48]. The conductivity of this surface reconstruc- tion is reported to beσBi√ 3× √ 3 = (1.4±0.1)×10−4 S/□ [6]. This value is in the range of typical TSS condu...
[12]

However, exact values for the surface conductivities of the respective (1 ×1) and (7×7) reconstructions have not yet been reported in the literature

Se/Si(111) Similar results as for the Te/Si(111) interface termi- nations can also be expected for Se-based van-der-Waals epitaxy on Si(111) [49–51]. However, exact values for the surface conductivities of the respective (1 ×1) and (7×7) reconstructions have not yet been repor...
[13]

It strongly depends both on the mate- rial system and the preparation parameters

Conclusion The interface conductivity can have a signiﬁcant inﬂu- ence on the overall current transport in a thin TI ﬁlm on a substrate. It strongly depends both on the mate- rial system and the preparation parameters. Reported literature values for reconstructed interfaces ar...
[14]

10, the band bending corre- sponding to case A is shown

Case A In the left panel of Fig. 10, the band bending corre- sponding to case A is shown. The surface potentials vtop and vbottom are either both positive (red solid line) or both negative (red dotted line) and exhibit only a small diﬀerence. If we choose z0 at the extremum (m...
[15]

Case B In case B (center panel of Fig. 10) there is no local extremum in the potentialv(z) because the diﬀerence be- tween the boundary valuesvtop andvbottom is larger than in case A, resulting in a more pronounced slope of the band potential. The calculation of the gate-depen...
[16]

Case C Case C is visualized in the right panel of Fig. 10. As vtop and vbottom have opposite signs, there must appear a root at a ﬁnite z between 0 and d. We identify this z with thez0 that separates the potential into two branches v1 and v2. In the thin TI ﬁlm, this root corr...
[17]

Transition between the cases A - C Starting from the symmetric case of band bending with vtop = vbottom, case A has to be applied if there is only a slight imbalance between vtop and vbottom that breaks the symmetry between the top and bottom surfaces of the ﬁlm. The transitio...
[18]

⏐⏐|vtop|−|vbottom| ⏐⏐≤ ∆, case A is used

When the absolute value of the diﬀerence betweenvtop andvbottom is smaller than ∆, i.e. ⏐⏐|vtop|−|vbottom| ⏐⏐≤ ∆, case A is used. When the diﬀerence is larger than ∆, i.e. ⏐⏐|vtop|−| vbottom| ⏐⏐> ∆, case B has to be applied. If the signs of vtop and vbottom become diﬀerent, th...
[19]

Hsieh, Y

D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Physical Review Letters 103, 146401 (2009)

2009
[20]

Roushan, J

P. Roushan, J. Seo, C. V. Parker, Y. S. Hor, D. Hsieh, D. Qian, A. Richardella, M. Z. Hasan, R. J. Cava, and A. Yazdani, Nature 460, 1106 (2009)

2009
[22]

Barreto, L

L. Barreto, L. K¨ uhnemund, F. Edler, C. Tegenkamp, J. Mi, M. Bremholm, B. B. Iversen, C. Frydendahl, M. Bianchi, and P. Hofmann, Nano Letters 14, 3755 (2014)

2014
[23]

Z. Ren, A. A. Taskin, S. Sasaki, K. Segawa, and Y. Ando, Physical Review B 82, 241306(R) (2010)

2010
[24]

S. Just, M. Blab, S. Korte, V. Cherepanov, H. Soltner, and B. Voigtl¨ ander, Physical Review Letters115, 066801 (2015)

2015
[25]

Miccoli, F

I. Miccoli, F. Edler, H. Pfn¨ ur, and C. Tegenkamp, Jour- nal of Physics: Condensed Matter 27, 223201 (2015)

2015
[26]

Voigtl¨ ander, V

B. Voigtl¨ ander, V. Cherepanov, S. Korte, A. Leis, D. Cuma, S. Just, and F. L¨ upke, Review of Scientiﬁc Instruments 89, 101101 (2018)

2018
[27]

Hofmann and J

P. Hofmann and J. W. Wells, J. Phys.: Condens. Matter 21, 013003 (2009)

2009
[28]

S. Just, H. Soltner, S. Korte, V. Cherepanov, and B. Voigtl¨ ander, Physical Review B95, 075310 (2017)

2017
[29]

Durand, X.-G

C. Durand, X.-G. Zhang, S. M. Hus, C. Ma, M. A. McGuire, Y.Xu, H. Cao, I. Miotkowski, Y. P. Chen, and A.-P. Li, Nano Lett. 16, 2213 (2016)

2016
[30]

L¨ upke, S

F. L¨ upke, S. Just, G. Bihlmayer, M. Lanius, M. Luys- berg, J. Doleˇ zal, E. Neumann, V. Cherepanov, I. Oˇ st´ adal, G. Mussler, D. Gr¨ utzmacher, and B. Voigtl¨ ander, Phys- ical Review B 96, 035301 (2017)

2017
[31]

D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, Nature Physics 8, 460 (2012)

2012
[32]

F. Yang, A. A. Taskin, S. Sasaki, K. Segawa, Y. Ohno, K. Matsumoto, and Y. Ando, ACS Nano 9, 4050 (2015)

2015
[33]

C. E. ViolBarbosa, C. Shekhar, B. Yan, S. Ouardi, E. Ike- naga, G. H. Fecher, and C. Felser, Physical Review B 88, 195128 (2013)

2013
[34]

Lanius, J

M. Lanius, J. Kampmeier, S. K¨ olling, G. Mussler, P. Koenraad, and D. Gr¨ utzmacher, Journal of Crystal Growth 453, 158 (2016)

2016
[36]

See Supplementary Material [url] for further details and examples about the general mechanism of band-bending in topological insulator materials
[37]

A. Many, Y. Goldstein, and N. Grover, Semiconductor Surfaces (North Holland, Amsterdam, 1965)

1965
[38]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature 438, 197 (2005)

2005
[39]

L¨ upke, S

F. L¨ upke, S. Just, M. Eschbach, T. Heider, E. M/suppress ly´ nczak, M. Lanius, P. Sch¨ uﬀelgen, D. Rosenbach, N. von den Driesch, V. Cherepanov, G. Mussler, L. Plucinski, D. Gr¨ utzmacher, C. M. Schneider, F. S. Tautz, and B. Voigtl¨ ander, npj Quantum Materials3, 46 (2018)

2018
[40]

Heinzel, Mesoscopic Electronics in Solid State Nanos- tructures, 3rd ed

T. Heinzel, Mesoscopic Electronics in Solid State Nanos- tructures, 3rd ed. (Wiley-VCH Verlag, Weinheim, 2010)

2010
[41]

Arakane, T

T. Arakane, T. Sato, S. Souma, K. Kosaka, K. Nakayama, M. Komatsu, T. Takahashi, Z. Ren, K. Segawa, and Y. Ando, Nature Communications 3, 636 (2012)

2012
[43]

P. D. C. King, R. C. Hatch, M. Bianchi, R. Ovsyannikov, C. Lupulescu, G. Landolt, B. Slomski, J. H. Dil, D. Guan, J. L. Mi, E. D. L. Rienks, J. Fink, A. Lindblad, S. Svens- son, S. Bao, G. Balakrishnan, B. B. Iversen, J. Oster- walder, W. Eberhardt, F. Baumberger, and P. Hofma...

2011
[47]

Brahlek, N

M. Brahlek, N. Koirala, N. Bansal, and S. Oh, Solid State Communications 215-216, 54 (2015)

2015
[48]

Brahlek, N

M. Brahlek, N. Koirala, M. Salehi, N. Bansal, and S. Oh, Physical Review Letters 113, 026801 (2014)

2014
[49]

Kellner, M

J. Kellner, M. Eschbach, J. Kampmeier, M. Lanius, E. M/suppress ly´ nczak, G. Mussler, B. Holl¨ ander, L. Plucinski, M. Liebmann, D. Gr¨ utzmacher, C. M. Schneider, and M. Morgenstern, Applied Physics Letters 107, 251603 (2015)

2015
[50]

L. He, X. Kou, M. Lang, E. S. Choi, Y. Jiang, T. Nie, 18 W. Jiang, Y. Fan, Y. Wang, F. Xiu, and K. L. Wang, Scientiﬁc Reports 3, 3406 (2013)

2013
[51]

Weyrich, M

C. Weyrich, M. Dr¨ ogeler, J. Kampmeier, M. Eschbach, G. Mussler, T. Merzenich, T. Stoica, I. E. Batov, J. Schu- bert, L. Plucinski, B. Beschoten, C. M. Schneider, C. Stampfer, D. Gr¨ utzmacher, and T. Sch¨ apers, Journal of Physics: Condensed Matter 28, 495501 (2016)

2016
[52]

Zhang, C.-Z

J. Zhang, C.-Z. Chang, Z. Zhang, J. Wen, X. Feng, K. Li, M. Liu, K. He, L. Wang, X. Chen, Q.-K. Xue, X. Ma, and Y. Wang, Nature Communications 2, 574 (2011)

2011
[53]

Satake, J

Y. Satake, J. Shiogai, D. Takane, K. Yamada, K. Fu- jiwara, S. Souma, T. Sato, T. Takahashi, and A. Tsukazaki, Journal of Physics: Condensed Matter 30, 085501 (2018)

2018
[54]

X. He, T. Guan, X. Wang, B. Feng, P. Cheng, L. Chen, Y. Li, and K. Wu, Applied Physics Letters 101, 123111 (2012)

2012
[55]

Koma, Thin Solid Films 216, 72 (1992)

A. Koma, Thin Solid Films 216, 72 (1992)

1992
[56]

Borisova, J

S. Borisova, J. Krumrain, M. Luysberg, G. Mussler, and D. Gr¨ utzmacher, Crystal Growth & Design 12, 6098 (2012)

2012
[57]

L¨ upke, S

F. L¨ upke, S. Korte, V. Cherepanov, and B. Voigtl¨ ander, Review of Scientiﬁc Instruments 86, 123701 (2015)

2015
[58]

Homoth, M

J. Homoth, M. Wenderoth, T. Druga, L. Winking, R. G. Ulbrich, C. A. Bobisch, B. Weyers, A. Ban- nani, E. Zubkov, A. M. Bernhart, M. R. Kaspers, and R. M¨ oller, Nano Letters9, 1588 (2009)

2009
[59]

Tanikawa, I

T. Tanikawa, I. Matsuda, T. Kanagawa, and S. Hasegawa, Physical Review Letters 93, 016801 (2004)

2004
[60]

Zhang, H

G. Zhang, H. Qin, J. Teng, J. Guo, Q. Guo, X. Dai, Z. Fang, and K. Wu, Applied Physics Letters 95, 053114 (2009)

2009
[61]

L¨ upke, J

F. L¨ upke, J. Doleˇ zal, V. Cherepanov, I. Oˇ st’´ adal, F. S. Tautz, and B. Voigtl¨ ander, Surface Science 681, 130 (2019)

2019
[62]

L¨ upke, M

F. L¨ upke, M. Eschbach, T. Heider, M. Lanius, P. Sch¨ uﬀelgen, D. Rosenbach, N. von den Dri- esch, V. Cherepanov, G. Mussler, L. Plucinski, D. Gr¨ utzmacher, C. M. Schneider, and B. Voigtl¨ ander, Nature Communications 8, 15704 (2017)

2017
[63]

Bauer and C

S. Bauer and C. A. Bobisch, Nature Communications 7, 11381 (2016)

2016
[64]

H. D. Li, Z. Y. Wang, X. Kan, X. Guo, H. T. He, Z. Wang, J. N. Wang, T. L. Wong, N. Wang, and M. H. Xie, New Journal of Physics 12, 103038 (2010)

2010
[65]

Sakamoto, T

Y. Sakamoto, T. Hirahara, H. Miyazaki, S. Kimura, and S. Hasegawa, Physical Review B 81, 165432 (2010)

2010
[66]

Hirahara, Y

T. Hirahara, Y. Sakamoto, Y. Takeichi, H. Miyazaki, S. Kimura, I. Matsuda, A. Kakizaki, and S. Hasegawa, Physical Review B 82, 155309 (2010)

2010
[67]

Bansal, Y

N. Bansal, Y. S. Kim, E. Edrey, M. Brahlek, Y. Horibe, K. Iida, M. Tanimura, G.-H. Li, T. Feng, H.-D. Lee, T. Gustafsson, E. Andrei, and S. Oh, Thin Solid Films 520, 224 (2011)

2011
[68]

R. D. Bringans and M. A. Olmstead, Physical Review B 39, 12985 (1989)

1989
[69]

S. Wu, Y. Zhou, Q.-H. Wu, C. Pakes, and Z.-Z. Zhu, Chemical Physics 382, 41 (2011)

2011
[70]

L. He, F. Xiu, Y. Wang, A. V. Fedorov, G. Huang, X. Kou, M. Lang, W. P. Beyermann, J. Zou, and K. L. Wang, Journal of Applied Physics 109, 103702 (2011). Parasitic conduction channels in topological insulator thin ﬁlms - Supplemental Material - Sven Just,1, 2, 3,∗ Felix L¨ upk...

2011 arXiv
[71]

E F t op = 20 meVE F t op = 47.5 meVE F t op = 240 meVE F t op = 212.5 meVE F t op = 185 meVE F t op = 157.5 meVE F t op = 130 meVE F t op = 102.5 meVE F t op = 75 meVE lectrons 0 5 01 001 502 002 501 08 1 09 1 01 01 01 11 01 2(b)H olesE F b ulk (meV) M obile hole density ph (cm-
[72]

E F t op = 20 meVE F t op = 47.5 meVE F t op = 240 meVE F t op = 212.5 meVE F t op = 185 meVE F t op = 157.5 meVE F t op = 130 meVE F t op = 102.5 meVE F t op = 75 meV FIG. 3. (Color online) Integrated mobile charge carrier densities for (a) electrons and (b) holes in a thin T...
[73]

E F t op (meV)E F b ottom (meV)1 08 1 09 1 01 01 01 11 01 2( a)( b)( c) 1 05 01 001 502 002 501 05 01 001 502 002 50H oles( b) p h (cm-
[74]

E F t op (meV)E F b ottom (meV)1 08 1 09 1 01 01 01 11 01 2( a)( b)( c) FIG. 4. (Color online) Color plot of the integrated mobile charge carrier densities for (a) electrons and (b) holes in a thin TI ﬁlm as function of Etop F and Ebottom F . All parameters of the calculation ...
[75]

Bianchi, D

M. Bianchi, D. Guan, S. Bao, J. Mi, B. B. Iversen, P. D. King, and P. Hofmann, Nature Communications 1, 128 (2010)

2010
[76]

D. Kong, J. J. Cha, K. Lai, H. Peng, J. G. Analytis, S. Meister, Y. Chen, H.-J. Zhang, I. R. Fisher, Z.-X. Shen, and Y. Cui, ACS Nano 5, 4698 (2011)

2011
[77]

J. G. Analytis, J.-H. Chu, Y. Chen, F. Corredor, R. D. McDonald, Z. X. Shen, and I. R. Fisher, Physical Review B 81, 205407 (2010)

2010
[78]

H. M. Benia, C. Lin, K. Kern, and C. R. Ast, Physical Review Letters 107, 177602 (2011)

2011
[79]

L¨ uth,Solid Surfaces, Interfaces and Thin Films , 6th ed

H. L¨ uth,Solid Surfaces, Interfaces and Thin Films , 6th ed. (Springer Verlag, Heidelberg, 2015)

2015
[80]

Haneman, Journal of Physics and Chemistry of Solids 11, 205 (1959)

D. Haneman, Journal of Physics and Chemistry of Solids 11, 205 (1959)

1959
[81]

Ryu, Journal of the Korean Physical Society 72, 122 (2018)

B. Ryu, Journal of the Korean Physical Society 72, 122 (2018)

2018
[82]

H. Qian, H. Tong, L. J. Zhou, B. H. Yan, H. K. Ji, K. H. Xue, X. M. Cheng, and X. S. Miao, Journal of Physics D: Applied Physics 49, 495302 (2016)

2016
[83]

J. H. Davies, The Physics of Low-dimensional Semiconductors (Cambridge University Press, 1997)

1997

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [21]

Zhang, C.-X

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Nature Physics 5, 438 (2009)

work page 2009

[2] [1]

It can be prepared at room temperature by depositing Te on top of a re- constructed Si(111)-(7×7) surface

Te/Si(111)-(7 ×7) For Te-based van-der-Waals epitaxy, a plausible inter- face reconstruction is the Te/Si(111)-(7 ×7) reconstruc- tion, which has been reported as a template for the growth of TI ﬁlms on Si(111) [42]. It can be prepared at room temperature by depositing Te on top of a re- constructed Si(111)-(7×7) surface. In a ﬁrst step, the (7×7)-reconst...

work page

[3] [2]

E F t op = 20 meVE F t op = 47.5 meVE F t op = 240 meVE F t op = 212.5 meVE F t op = 185 meVE F t op = 157.5 meVE F t op = 130 meVE F t op = 102.5 meVE F t op = 75 meV Majority carriers: electrons Majority carriers: holes1 01 8n b ulk ( c m-

work page

[4] [3]

pb ulk ( c m- 3) FIG. 5. (Color online) Integrated total mobile charge car- rier density nﬁlm based on the symmetric approximation for a thin TI ﬁlm as function of the dopant concentration rep- resented by the bulk Fermi energy Ebulk F . The surface Fermi energy Etop F is an additional parameter. For Ebulk F inside the band-gap, the calculated ﬁlm carrier...

work page

[5] [4]

This is immediately obvious from Eq

Screening The weak band bending in the thin TI ﬁlm is linked to the long screening length L compared to the small ﬁlm thickness d. This is immediately obvious from Eq. (2), which shows that the curvature of the band bending potential v is inversely proportional to the square of L. A small curvature of course also limits the value of v that can be reached ...

work page

[6] [5]

4, only non-degenerate doping levels in the TI have been considered, all of which apparently lead to a downward band bending

Degenerate doping In Fig. 4, only non-degenerate doping levels in the TI have been considered, all of which apparently lead to a downward band bending. Of course, it is in principle also possible that the dopant concentration is suﬃciently high for the TI material to be degenerately n-doped, with Ebulk F above the conduction band edge. According to our ca...

work page

[7] [6]

BiSbTe 3, which was studied extensively in ref

The example of BiSbTe 3 Here, we focus on the speciﬁc TI material (Bi1−xSbx)2Te3 with x = 0 .5, i.e. BiSbTe 3, which was studied extensively in ref. [21, 31]. Fig. 4 that we used above to illustrate generic properties of band bending in thin TI ﬁlms, was already calculated for this case. The assumption of a ﬁxed Etop F in Fig. 4 (a) to (c) corresponds to ...

work page

[8] [7]

Mobile charge carrier density Within the Boltzmann approximation, the mobile charge carrier density can be calculated from the po- tential v(z) by ne(z) = nb exp[v(z)] and ph(z) = pb exp[−v(z)] for electrons and holes, respectively. In- tegrating the sum of ne(z) and ph(z) over the thickness d of the thin ﬁlm results in the total mobile charge carrier den...

work page