Unveiling the Key Factors that Limit Carrier Transport in Ultra‑Thin Amorphous Sn‑Doped In₂O₃ Films with Superior Hall Mobility

Abstract

We demonstrate that mass density and size effects are the primary factors limiting carrier transport in ultra‑thin amorphous Sn‑doped In₂O₃ (a‑ITO) films. a‑ITO layers with thicknesses (t) from 5 to 50 nm were deposited on non‑alkali glass by reactive plasma deposition (RPD) without intentional substrate heating. For films thicker than 10 nm, Hall mobility (µH) exceeded 50 cm² V⁻¹ s⁻¹, while a 5‑nm film maintained a µH above 40 cm² V⁻¹ s⁻¹. X‑ray reflectivity (XRR) revealed that mass density (dm) governs carrier transport: dm ≈ 7.2 g cm⁻³ for t > 10 nm, versus 6.6–6.8 g cm⁻³ for t < 10 nm. We provide quantitative insight into the size effect for films thinner than 10 nm, showing that the ratio of t to the electron mean free path (λ) controls µH.

Introduction

Sn‑doped indium oxide (ITO) remains the benchmark transparent conducting oxide (TCO) for photovoltaic and optoelectronic devices. In₂O₃ crystallizes in a bixbyite lattice (space group Ia‑3), featuring corner‑sharing InO₆ octahedra that facilitate high carrier mobility through substantial 5s/5p orbital overlap. Recent studies have achieved Hall mobilities > 100 cm² V⁻¹ s⁻¹ in hydrogenated or Ce‑doped In₂O₃ polycrystalline films, expanding the transparent window into the near‑infrared.

Typical TCO layers exceed 50 nm in thickness to maintain low sheet resistance, yet ultra‑thin TCOs (t < 50 nm) are attractive for anti‑reflection coatings but suffer from increased resistance. Early reports on very thin amorphous ITO (a‑ITO) films showed a sharp decline in µH below 20 nm, with critical thicknesses around 4 nm for sputtered and pulsed‑laser deposition (PLD) growths.

Carrier scattering in degenerate polycrystalline ITO has been attributed to grain boundaries and intragrain centers (phonons, ionized and neutral impurities). In contrast, a‑ITO lacks grain boundaries; its transport is governed by the random In–O network with short‑range order. While defect models have been applied to a‑IZO and crystalline In₂O₃, a systematic study linking mass density, structural features, and transport in very thin a‑ITO is lacking.

Here we employ reactive plasma deposition (RPD) with direct‑current arc discharge, a high‑rate, large‑area deposition technique, to fabricate uniform a‑ITO films down to 5 nm. RPD enables reliable evaluation of transport properties in ultra‑thin films, paving the way for high‑µH TCOs.

Method

a‑ITO films were grown on Corning Eagle XG glass by RPD (Sumitomo Heavy Industries). The plasma, generated by an electropositive Ar⁺ source (Uramoto gun), ablates a sintered target of In₂O₃ (5 wt.% SnO₂, 4.6 at.% Sn). Ar flow rates were 25 sccm (chamber) and 40 sccm (gun). Oxygen flow rates (OFR) of 20 or 30 sccm were used; substrates were maintained below 70 °C. The growth pressure was 0.3 Pa and the typical deposition rate 3.6 nm s⁻¹. Film thickness (t) was tuned by adjusting substrate travel speed.

Schematic diagram of RPD with DC arc discharge

X‑ray diffraction (XRD) and X‑ray reflectivity (XRR) were performed on a Rigaku ATX‑G diffractometer (Cu‑Kα, λ = 0.15405 nm). XRR data provided film thickness and mass density (dm) via a two‑layer model (film + rough interface). Roughness values (rs, ri) were ≈ 1 nm. Stylus profiling (Dektak 6M) confirmed thicknesses. Electrical properties were measured at room temperature using a van der Pauw geometry (Nanometrics HL5500PC).

RPD is a mass‑production technique with <± 5 % uniformity and reproducibility for thickness and transport properties, ensuring high reliability of single‑point measurements.

Results and Discussion

Mass Density of a‑ITO Films

All XRD patterns were amorphous, confirming the a‑phase. XRR curves fitted the two‑layer model with excellent agreement (Fig. 2). Table 1 lists t, dm, rs, and ri; thicknesses matched stylus measurements. Figure 3 shows dm versus t: films > 10 nm have dm ≈ 7.2 g cm⁻³ (bulk value), while t < 7 nm films exhibit a sharp drop to 6.6–6.8 g cm⁻³, independent of OFR.

XRR data (crosses, circles, triangles) and fitted curves (solid lines) of a‑ITO films with thicknesses 5.1, 20.9, and 47.6 nm grown at an OFR of 20 sccm

Mass density dm derived from XRR results of a‑ITO films grown at an OFR of 20 sccm (triangles) or 30 sccm (circles) as a function of film thickness t

Transport Properties

Figure 4 presents resistivity (ρ), carrier density (ne), and µH for films grown at 20 and 30 sccm. At a given t, ne is higher for 20 sccm while µH is lower, indicating ionized impurity scattering as a key factor. For t < 30 nm, µH increases with ne, suggesting an additional size‑related mechanism.

a Electrical resistivity ρ, b carrier concentration ne, and c Hall mobility µH of a‑ITO films grown at an OFR of 20 sccm (triangles) or 30 sccm (circles) as functions of thickness t. All values were obtained at room temperature

Sputtering and PLD studies report a critical thickness of ~ 4 nm where 3D island coalescence is incomplete, leading to a steep drop in µH. In contrast, our RPD films show a < 30 % decrease in µH at 5 nm relative to > 10 nm films, indicating a 2D growth mode that mitigates size‑induced scattering.

Dominant Factors Determining µH: Mass Density and Mean Free Path

Figure 5 reveals a strong positive correlation (R = 0.73) between µH and dm for both OFRs. Simulations of grazing‑incidence X‑ray scattering suggest that a‑In₂O₃ contains more corner‑sharing In–O–In bonds than crystalline In₂O₃. In ultra‑thin a‑ITO, additional oxygen vacancies (Vadd) promote a transition from edge‑sharing to corner‑sharing polyhedra, increasing In–In distances and reducing orbital overlap, thereby localizing carriers and lowering ne and µH.

Relationship between Hall mobility µH and mass density dm of a‑ITO films grown at an OFR of 20 sccm (triangles) or 30 sccm (circles). The solid line represents a linear fit to all data points.

Models of local structure: a) crystalline ITO, b) a‑ITO, and c) very thin a‑ITO with added Vadd, illustrating the transition from edge‑sharing to corner‑sharing.

For t < 10 nm, we also examined the electron mean free path (λ). Using λ = µh/(2e) (3ne/π)¹⁄³, we found λ rises sharply up to 10 nm and then plateaus. Plotting µH versus t/λ (Fig. 7b) shows a clear kink at t/λ ≈ 2, i.e., t ≈ 10 nm. This indicates that when λ approaches t, surface and interface scattering become dominant, further limiting µH in the thinnest films.

a Mean free path λ versus film thickness t and b relationship between Hall mobility µH and the ratio t/λ for a‑ITO films grown at an OFR of 20 sccm (triangles) or 30 sccm (circles). The solid line [A] and dot‑dashed line [B] denote linear fits for t = 5–10 nm and t = 10–50 nm, respectively. Correlation coefficients R are specified.

Conclusion

We have successfully fabricated ultra‑thin a‑ITO films (t < 50 nm) on glass with Hall mobilities exceeding 40 cm² V⁻¹ s⁻¹, leveraging RPD’s high‑rate, 2D‑growth capability. The dominant limitation to carrier transport is the film’s mass density, which reflects the proportion of corner‑sharing In–O polyhedra within the edge‑sharing network. For films thinner than 10 nm, transport is further constrained by the ratio of film thickness to electron mean free path, highlighting the importance of surface and interface scattering. Future work will focus on elucidating the crystallographic evolution of a‑ITO as a function of thickness to guide the design of next‑generation high‑µH TCOs.

Abbreviations

2D:

Two dimensional

3D:

Three dimensional

a‑In₂O₃:

Amorphous-phase indium oxide

a‑ITO:

Amorphous-phase tin‑doped indium oxide

a‑IZO:

Amorphous-phase zinc‑doped indium oxide

DC:

Direct current

ITO:

Tin‑doped indium oxide

MFP:

Mean free path of carriers

OFR:

Oxygen flow rate during deposition

PLD:

Pulsed‑laser deposition

RPD:

Reactive plasma deposition

TCO:

Transparent conducting oxide

Vadd:

Added O vacancy defect

Vstr:

Structural vacancy

XRD:

X‑ray diffraction

XRR:

X‑ray reflectivity