The wide-gap semiconducting perovskite BaSnO3 has attracted attention since the discovery of outstanding mobility at high electron densities, spurred on by potential applications in oxide, transparent, and power electronics. Despite progress, much remains to be understood in terms of mobility-limiting scattering in BaSnO3 thin films and thus mobility optimization. Here, we apply solid-state ion-gel-based electrolyte gating to electrostatically control electron density over a wide range (1018 cm−3 to >1020 cm−3) in BaSnO3 films. Temperature- and gate-voltage-dependent transport data then probe scattering mechanisms and mobility vs electron density alone, independently of sample-to-sample defect density variations. This is done on molecular-beam-epitaxy- and sputter-deposited films as a function of thickness, initial chemical doping, and initial mobility. Remarkably universal behavior occurs, the mobility first increasing with electron density to ∼1020 cm−3 before decreasing slightly. This trend is quantitatively analyzed at cryogenic and room temperatures using analytical models for phonon, ionized impurity, charged dislocation, surface/interface roughness, and electrolyte-induced scattering. The mobility maximum is thus understood to arise from competition between charged impurity/dislocation scattering and electrolyte scattering. The gate-voltage-induced mobility enhancement is found as large as 2000%, realizing 300 K mobility up to 140 cm2 V−1 s−1. This work thus significantly advances the understanding of mobility-limiting scattering processes in BaSnO3, resulting in outstanding room temperature mobilities.

The wide-bandgap perovskite oxide semiconductor BaSnO3 (BSO) was discovered in 2012 to support room temperature electron mobility (μ) up to 320 cm2 V−1 s−1 in single crystals and to maintain such mobilities to unusually high electron density (n).1–3 The outstanding 300 K mobility is thought to result from a dispersive Sn 5s conduction band in combination with low phonon scattering rates,4–8 suggesting applications in oxide, transparent, and power electronics.1,2,9–17 BSO thin films have thus become of high interest, n-doping being achieved via La1,2,9–19 and rare-earth20,21 substitution for Ba (LaBa and NdBa), Sb substitution for Sn (SbSn),22,23 and oxygen vacancies (VO).21,24,25 The lack of commercial substrates (particularly perovskites) around the 4.116 Å BSO lattice parameter has necessitated the use of substrates with a significant lattice and/or symmetry mismatch,1,2,9–12,14–17,20,22–25 however, generating high misfit and threading dislocation densities and limiting μ. Pulsed laser deposition,1,2,9,10,16,17,20,22,23 sputtering,24–26 and molecular beam epitaxy (MBE)11,12,14,15 have been applied, the latter generating the highest 300 K mobilities (120 cm2 V−1 s−1–183 cm2 V−1 s−111,14,15), although these remain only half those of bulk crystals.

In light of the above, substantial efforts have been undertaken to understand scattering in BSO films and thus to optimize mobility.1,2,9–11,13–17,23–25 A central finding is substantial improvement in μ with increasing n, typically achieved by varying [La] or [VO]. Scaling of the form μ ∝ nm has been found up to ∼1020 cm−3, with m varying from 0.5 to 2,19,25 followed by a decrease in μ at the highest n.19,25 The improvement in μ with doping is typically interpreted in terms of screening of a dominant density of charged defects,1,2,9,11,14,15,23–25 particularly dislocations arising from a significant lattice mismatch.1,2,9,11,14,15,23–25,27 The deterioration in μ at the highest n is then interpreted as a crossover to dominant ionized impurity scattering.14 Non-stoichiometry-related point defects (e.g., VBa and VO) and stacking defects also affect μ in BSO.14,15,28

The difficulty of such studies, which require sample sets with varied doping but minimal variations in other defect densities, along with the interest in BSO transistors, has naturally led to electrostatic doping of BSO.29–39 Electrolyte gating in electric double layer transistors (EDLTs) is powerful in this context. In EDLTs, the dielectric in a field-effect transistor (FET) is replaced with an electrolyte, often an ionic liquid.40–42 Application of a gate voltage (Vg) drives electrolyte cations/anions to the interface with the gated material, generating a two-dimensional (2D) sheet of electrons/holes and forming a nanoscopic electric double layer (EDL) with a very large specific capacitance (10 µF cm−2–100 µF cm−2).40–42 This translates to 1014 cm−2–1015 cm−2 electron/hole densities at just a few volts, 10–100 times above conventional FETs.41,42 Electrostatic doping over extreme carrier density ranges is thus enabled, although deconvolution of electrostatic and electrochemical gating mechanisms is essential.42 

At least two prior studies have focused on BSO EDLTs.31,37 In 2017, Fujiwara et al. reported on ionic-liquid-gated PLD-grown undoped BSO, observing an insulator–metal transition (IMT) at high Vg and thickness.31 μ ∝ n1.5 was observed for 3D densities in the accumulation layer of ∼1020 cm−3, followed, intriguingly, by a decrease in μ at the highest n.31 The same non-monotonicity in μ(n) as in chemically doped films thus occurs, despite the electrostatic (i.e., nominally ionized-impurity-free) doping. Gate-enhanced μ up to 220 cm2 V−1 s−1 was achieved at 150 K, although 300 K data were not acquired due to leakage problems.31 Our own recent work (Ref. 37) expanded upon this, applying ion-gel-based electrolyte gating to sputtered BSO with varied thicknesses and initial chemical doping. Significantly, highly reversible gating was obtained over an exceptional Vg range (±4 V), even at 300 K, with undetectable structural modifications in operando synchrotron x-ray diffraction (XRD).37 Essentially ideal electrostatic response was thus achieved in electrolyte-gated BSO, in sharp contrast with the (often VO-based) electrochemical response in many oxides.42 The extraordinarily low VO diffusivity in BSO was advanced as the origin of this, restricting Vg-induced VO motion and resulting in reversible electrostatic electron doping.37 This was then exploited to span strongly localized, weakly localized, and metallic regimes, attaining ∼1014 cm−2 2D electron density, Vg-induced mobility enhancement up to 2400%, and μ = 51.4 cm2 V−1 s−1 at 300 K in sputtered films.37 Two-channel-conduction analysis based on self-consistent Schrödinger–Poisson modeling was also established, enabling a quantitative extraction of μ at the gated surface, even in chemically doped films, where the film bulk shunts current.37 

Based on the above discussion, the understanding is in place for a wide-ranging quantitative study of the temperature (T)-dependent μ(n) relation in electrostatically doped BSO, potentially elucidating mobility-limiting scattering sources, the maximal Vg-induced 300 K mobility enhancement, and the non-monotonic μ(n). The latter is of general interest in EDLTs, possible origins of a downturn at high n including Coulombic disorder from the EDL, surface/interface scattering, and roughness effects.40,43,44 We address these issues here through solid electrolyte (ion-gel-based) gating of sputtered and MBE-grown BSO epilayers with varied thicknesses, buffer layer, and initial chemical doping. Wide T- and Vg-range data demonstrate that μ at the gated surface increases with the induced 3D electron density up to ∼1020 cm−3, before weakly decreasing at the highest n. Modeling of phonon, ionized impurity, charged dislocation, interface roughness, and electrolyte (i.e., EDL-induced) scattering reveals the dominance of charged dislocations and ionized impurities at low and moderate n, crossing over to electrolyte-limited mobility at high n. The end result is Vg-induced μ enhancement up to 2000% across an IMT in lightly chemically doped BSO and a maximum gated μ of 140 cm2 V−1 s−1 in heavily chemically doped MBE-grown BSO. The latter is comparable to the highest mobilities reported in BSO films, highlighting the efficacy of electrolyte gating.

Epitaxial La- and VO-doped BSO films were grown by high pressure oxygen sputter deposition and hybrid MBE, as reported previously.14,24,25,37,45 Briefly, 51-nm-thick La0.02Ba0.98SnO3 films were DC sputtered at 850 °C in 1.9 Torr of O2 from a nominally stoichiometric ceramic La0.02Ba0.98SnO3 target.37 VO-doped films were obtained by vacuum annealing undoped BSO, which was RF sputtered at 750 °C in 1.5 Torr of O2 from a nominally stoichiometric BSO target.24 The resulting 300 K initial 3D Hall electron density (n0) increases with annealing temperature and thickness,25 reaching 1.7 × 1019 cm−-3 and 4.1 × 1019 cm−3 in 10-nm- and 12-nm-thick films after a 900 °C, 4 h anneal at <10−7 Torr. 54-nm-thick sputtered undoped BSO films were also vacuum annealed at a lower temperature of 475 °C to achieve 300 K n0 as low as 1.8 × 1018 cm−3. The sputtered films thus span 1.8 × 1018 cm−3–8.0 × 1019 cm−3 initial 300 K electron density. In terms of MBE (see Ref. 45), 51-nm-thick nominally undoped BSO was grown, in addition to 30-nm-thick LaxBa1−xSnO3 on 30- to 114-nm-thick undoped BSO buffer layers, as depicted in Fig. 1(a). We define dactive and dbuffer as the thicknesses of the active (doped) and buffer (undoped) layers, respectively. All films were grown on LaAlO3(001) or GdScO3(001) substrates (SrTiO3 was avoided to circumvent substrate VO issues) and are relaxed at these thicknesses.24,25,45 Extensive structural characterization via high-resolution (and synchrotron37) XRD,14,24,25,45 scanning transmission electron microscopy (STEM),24,25,27 electron energy loss spectroscopy,46 energy dispersive x-ray spectroscopy,24 grazing-incidence x-ray reflectivity,24,25,37,45 and atomic force microscopy14,24,25,37,45 has been published, establishing phase-pure, relaxed, smooth, epitaxial films.

FIG. 1.

Schematics of (a) a LaAlO3(001)/BaSnO3(buffer)/LaxBa1−xSnO3 heterostructure and (b) the ion-gel-gate device employed. Shown are the 5 × 5 mm2 LaAlO3(001) substrate (gray), the 1 × 1 mm2 LaxBa1−xSnO3−δ channel (purple), the ion gel (transparent) covering the channel and gate electrodes, and the Ti/Au electrodes (gold). Four electrodes are used for the van der Pauw measurement of the film (I and V are the excitation current and voltage, respectively), and two electrodes (shorted together) are used to apply the gate voltage (Vg).

FIG. 1.

Schematics of (a) a LaAlO3(001)/BaSnO3(buffer)/LaxBa1−xSnO3 heterostructure and (b) the ion-gel-gate device employed. Shown are the 5 × 5 mm2 LaAlO3(001) substrate (gray), the 1 × 1 mm2 LaxBa1−xSnO3−δ channel (purple), the ion gel (transparent) covering the channel and gate electrodes, and the Ti/Au electrodes (gold). Four electrodes are used for the van der Pauw measurement of the film (I and V are the excitation current and voltage, respectively), and two electrodes (shorted together) are used to apply the gate voltage (Vg).

Close modal

EDLTs [Fig. 1(b)] were fabricated using similar methods to prior work.37 1 × 1 mm2 channels were defined by Ar milling using steel masks, followed by definition of Ti (20 nm)/Au (60 nm) sample and side-gate electrodes. “Cut and stick” solid-state ion gels47 were employed based on the ionic liquid 1-ethyl-3-methylimidazolium bis(triflouromethylsulfonyl)amide in a matrix of poly(vinylidene fluoride-co-hexafluoropropylene). van der Pauw resistance measurements were made DC, with a Keithley 2400 source-measure unit or a Keithley 220 current source and 2002 voltmeter, using currents that avoided non-ohmicity and self-heating. 2 K–300 K measurements were then made in magnetic fields to 90 kOe in a Quantum Design Physical Property Measurement System. Gate voltages were applied at 300 K for ∼30 min before cooling to the desired measurement temperature; T-dependent data were taken on subsequent warming.

We first present data on an MBE-grown LaAlO3(001)/BaSnO3 (114 nm)/LaxBa1−xSnO3 (29 nm) film, where the high dbuffer optimizes μ0 (initial mobility),14 and the intermediate dactive of 29 nm reflects a compromise between improved μ0 at higher dactive14 and the need to minimize dactive to maximize transport modulation by EDLT surface gating.37 We obtained 300 K values of n0 = 3.5 × 1019 cm−3 and μ0 = 91 cm2 V−1 s−1. As shown in Fig. 2(a), such films are already metallic at Vg = 0 with a sheet resistance (RS) well below h/e2 ≈ 26 kΩ and dRS/dT > 0 over a wide range. Positive gate voltages are of highest interest here, as they lead to electron accumulation and thus μ enhancement. (Depletion at negative Vg was studied in initially metallic sputtered films in prior work, inducing a crossover to weak and then strong localization.37) From Fig. 2(a), positive Vg up to 3 V induces a gradual RS decrease (up to ∼50% at low T), the weak low T upturn in RS(T) eventually being essentially extinguished. Further increasing Vg to 4 V (the limit of electrochemical stability of the ion gel48), however, results in only a slight additional change in RS(T). We note parenthetically that the fluctuations in RS(T) above ∼175 K, which are common in EDLTs, are associated with the onset of ionic mobility in the ion gel.37,49,50

FIG. 2.

(a) Temperature (T) dependence of the sheet resistance (RS) at multiple (positive) gate voltages (Vg) for a LaAlO3(001)/BaSnO3 (114 nm)/LaxBa1−xSnO3 (29 nm) MBE-grown film. [(b) and (c)] The corresponding Vg dependence of the apparent 3D Hall electron density (nH) and apparent Hall mobility (μH) at 300 K, 150 K, and 10 K. [(d) and (e)] The corresponding Vg dependence of the extracted accumulation layer 3D electron density (nA) and mobility (μA) at 300 K and 10 K. The inset in (d) shows the corresponding calculated accumulation layer thickness (dA).

FIG. 2.

(a) Temperature (T) dependence of the sheet resistance (RS) at multiple (positive) gate voltages (Vg) for a LaAlO3(001)/BaSnO3 (114 nm)/LaxBa1−xSnO3 (29 nm) MBE-grown film. [(b) and (c)] The corresponding Vg dependence of the apparent 3D Hall electron density (nH) and apparent Hall mobility (μH) at 300 K, 150 K, and 10 K. [(d) and (e)] The corresponding Vg dependence of the extracted accumulation layer 3D electron density (nA) and mobility (μA) at 300 K and 10 K. The inset in (d) shows the corresponding calculated accumulation layer thickness (dA).

Close modal

The corresponding Vg-dependent measurements of the apparent 3D Hall electron density (i.e., nH = −1/RHe, where RH is the Hall coefficient assuming the full film thickness) are shown at 300 K, 150 K, and 10 K in Fig. 2(b). nH increases roughly linearly with Vg at all T, from ∼3.25 × 1019 cm−3 to ∼4.50 × 1019 cm−3, the weak T dependence being consistent with degenerate transport at these dopings.14,25 As shown in Fig. 2(c), the resulting apparent Hall mobility (μH) increases with Vg up to 3 V, followed by saturation (at 300 K) or a decrease (at 10 K and 150 K) at 4 V. While mobility thus generally increases with Vg (and with electron density), it is vital to understand that, in chemically doped films, the apparent nH and μH do not reflect the values in the accumulation layer at the BSO/electrolyte interface due to current shunting by the film “bulk.” As shown in detail in our prior work,37 this can be addressed through two-channel (surface/bulk) conduction modeling, where the 3D electron density and mobility in the accumulation layer (nA, μA) are related to the apparent 2D Hall electron density and mobility (nH2D, μH2D) via37,51

nH2DμH=nAμAdA+nBμBdB,
(1a)
nH2DμH2=nAμA2dA+nBμB2dB.
(1b)

Here, nB and μB are the 3D carrier density and mobility in the “bulk” (i.e., under the accumulation layer), where Vg does not affect transport, meaning that nB = n0 and μB = μ0. The thicknesses of the accumulation (dA) and bulk (dB) regions also appear in Eq. (1), obeying dA + dB = dactive. Extraction of nA and μA thus requires determination of dA, which we define as the thickness of the region in which 90% of the Vg-induced electrons are confined.37 This dA can then be determined from induced electron density depth profiles, calculated from self-consistent Schrödinger–Poisson analysis.37,52

The Vg-dependent nA and μA extracted in this way are shown in Figs. 2(d) and 2(e) based on the calculated dA(Vg) in the inset of Fig. 2(d). As Vg is increased, dA, of course, shrinks (to 4.6 nm at 4 V) due to increased confinement at high gate electric fields. The resulting 3D nA values increase from ∼3.5 × 1019 cm−3 to ∼1.3 × 1020 cm−3, the T independence reflecting degenerate doping. Notably, despite nA being increased by only a factor of ∼4 (due to high initial doping), μA increases significantly [Fig. 2(e)]. Vg = 3 V, in fact, induces 53% and 82% increases in μA at 300 K and 10 K, respectively, reaching 140 cm2 V−1 s−1 and 281 cm2 V−1 s−1. This represents the highest 300 K mobility in electrolyte-gated BSO, 140 cm2 V−1 s−1 being one of the largest BSO film values reported in any context. Notably, and as returned to below, at the highest Vg of 4 V, the saturation or drop in μH [Fig. 2(c)] is preserved in μA [Fig. 2(e)]. As shown in Fig. S1 of the supplementary material, similar behavior is found in other buffered MBE-grown films, such as a LaAlO3(001)/BaSnO3 (30 nm)/LaxBa1−xSnO3 (30 nm) film. The latter has μ0 = 70 cm2 V−1 s−1 at 300 K, reaching 102 cm2 V−1 s−1 at Vg = 3 V, before decreasing. In general, the highest fully gated mobilities in this work were obtained at high dbuffer (≳100 nm), and reasonably high dactive (≳30 nm), due to challenges in minimizing dislocation densities (see below). At such dactive values, two-channel conduction analysis is essential.

As a contrasting example, highlighted in Fig. 3 is a film with much lower initial doping and mobility. This sputtered LaAlO3(001)/BaSnO3−δ (54 nm) film has n0 = 1.8 × 1018 cm−3 and μ0 = 2 cm2 V−1 s−1 at 300 K and is initially insulating, with RS (300 K) = 3.4 × 105 Ω/sq and large, negative dRS/dT [Fig. 3(a)]. Similar behavior was shown in our prior work to be due to variable-range hopping.37 More important in the current context, the lower n0 leads to a more dramatic influence of Vg, 4 V inducing an IMT to a state with minimum RS ≈ 7900 Ω/sq (<h/e2) and weak RS(T). Again, fluctuations in RS(T) above 175 K are associated with the onset of ionic mobility in the ion gel. As shown in Figs. 3(b) and 3(c), the apparent nH and μH increase with Vg, but with distinctly different behavior to Fig. 2. nH is now strongly non-linear, being quite flat to ∼2 V (essentially a threshold voltage) before increasing rapidly. μH shows a corresponding rapid increase above ∼2 V, the fractional gate-induced mobility enhancement being much larger than in Fig. 2. We ascribe this to an initial insulating state with substantial disorder, compensation, and trap states, the rapid increase in nH and μH occurring when diffusive, and eventually metallic transport is induced, as the Fermi level approaches the mobility edge and conduction band minimum.37 Self-consistent Schrödinger–Poisson analysis for this film results in dA(Vg) shown in the inset of Fig. 3(d), the larger Vg = 0 values than Fig. 2(d) arising due to lower n0. Two-channel modeling yields the Vg-dependent nA and μA shown in Figs. 3(d) and 3(e) at 300 K and 50 K; the latter is the lowest T at which Hall data could be acquired, even then only at 2 V and above. The overall behavior is notably similar to Figs. 3(b) and 3(c), particularly at high Vg, due to the dominance of the gate-induced electron density over n0. At Vg = 4 V, the 3D nA reaches ∼9 × 1019 cm−3 (independent of T due to gate-induced degenerate doping), meaning that the probed 3D electron density range becomes almost 1018 cm−3 to 1020 cm−3 in this single film. The increase in μA (300 K) amounts to 2000%, reaching 40 cm2 V−1 s−1 in this sputtered LaAlO3(001)/BaSnO3−δ (54 nm) film. As shown in Fig. S2 of the supplementary material, films with no intentional doping can also be gated through an IMT, an MBE-grown LaAlO3(001)/BaSnO3 (51 nm) film turning on at Vg = 3 V and reaching 100 cm2 V−1 s−1 at 50 K and 4 V. Nevertheless, maximum gated mobilities in this study were obtained with initially chemically doped films.

FIG. 3.

(a) Temperature (T) dependence of the sheet resistance (RS) at multiple (positive) gate voltages (Vg) for a LaAlO3(001)/BaSnO3−δ (54 nm) sputter-deposited film. [(b) and (c)] The corresponding Vg dependence of the apparent 3D Hall electron density (nH) and apparent Hall mobility (μH) at 300 K, 150 K, and 50 K. [(d) and (e)] The corresponding Vg dependence of the extracted accumulation layer 3D electron density (nA) and mobility (μA) at 300 K and 50 K. The inset in (d) shows the corresponding calculated accumulation layer thickness (dA).

FIG. 3.

(a) Temperature (T) dependence of the sheet resistance (RS) at multiple (positive) gate voltages (Vg) for a LaAlO3(001)/BaSnO3−δ (54 nm) sputter-deposited film. [(b) and (c)] The corresponding Vg dependence of the apparent 3D Hall electron density (nH) and apparent Hall mobility (μH) at 300 K, 150 K, and 50 K. [(d) and (e)] The corresponding Vg dependence of the extracted accumulation layer 3D electron density (nA) and mobility (μA) at 300 K and 50 K. The inset in (d) shows the corresponding calculated accumulation layer thickness (dA).

Close modal

Further understanding of mobility-limiting scattering mechanisms in these films is facilitated by Figs. 4(a) and 4(b), which plot low and high temperature μA vs nA for seven ion-gel-gated films (four sputtered and three MBE) with widely varied dactive, dbuffer, n0, and μ0. (Vg is, of course, the implicit variable here.) The low T regime in Fig. 4(a) corresponds to 2 K–50 K, dependent on the lowest T that could be probed in each film, while Fig. 4(b) corresponds to 300 K. Despite the different growth methods, substrates, dactive, dbuffer, n0, and μ0, the qualitative behavior is essentially universal: μA increases with nA as a power law up to ∼1020 cm−3AnAm with m ≈ 0.5–0.8 at low and high T), before decreasing slightly in the highest mobility films. As already noted, such non-monotonic μ(n) in chemically doped BSO films is ascribed to an improved screening of the charged dislocations with increasing n, giving way at high n to dominant ionized impurity scattering (with μ ∝ 1/ND ≈ 1/n, where ND is the donor density).5,14 In electrostatically doped BSO, non-monotonicity in μ(n) remains,31 despite that n is increased independent of ND, indicating that some other scattering source limits μ at high n.

FIG. 4.

[(a) and (b)] Low temperature (T = 2 K–50 K) and room temperature (300 K) dependence of the extracted accumulation layer mobility (μA) on the accumulation layer 3D electron density (nA). Data (colored solid points) are shown for both MBE- and sputter-deposited films, with various thicknesses, and La or oxygen vacancy doping, as in the legend. The fits (colored solid lines) are based on the model discussed in the text. For the illustrative case of the highest mobility LaAlO3(001)/BaSnO3 (114 nm)/LaxBa1−xSnO3 (29 nm) film (green points), the extracted mobilities associated with scattering due to ionized impurities (μii), charged threading dislocations (μdisl), surface roughness (μroughness), the ion gel (μion gel), and phonons (μphonon) are shown by colored dashed lines. Temperatures between 2 K and 50 K are shown in (a) based on the lowest T to which each device could be measured; no data are shown for LaAlO3(001)/BaSnO3−δ (10 nm) due to prohibitively large resistances. (c) Extracted dislocation density (Ndisl) vs dtot, where dtot = dactive + dbuffer is the total thickness for both sputtered and MBE-grown films.

FIG. 4.

[(a) and (b)] Low temperature (T = 2 K–50 K) and room temperature (300 K) dependence of the extracted accumulation layer mobility (μA) on the accumulation layer 3D electron density (nA). Data (colored solid points) are shown for both MBE- and sputter-deposited films, with various thicknesses, and La or oxygen vacancy doping, as in the legend. The fits (colored solid lines) are based on the model discussed in the text. For the illustrative case of the highest mobility LaAlO3(001)/BaSnO3 (114 nm)/LaxBa1−xSnO3 (29 nm) film (green points), the extracted mobilities associated with scattering due to ionized impurities (μii), charged threading dislocations (μdisl), surface roughness (μroughness), the ion gel (μion gel), and phonons (μphonon) are shown by colored dashed lines. Temperatures between 2 K and 50 K are shown in (a) based on the lowest T to which each device could be measured; no data are shown for LaAlO3(001)/BaSnO3−δ (10 nm) due to prohibitively large resistances. (c) Extracted dislocation density (Ndisl) vs dtot, where dtot = dactive + dbuffer is the total thickness for both sputtered and MBE-grown films.

Close modal

To quantitatively understand mobility-limiting scattering sources, we utilize analytical models for charged dislocation, ionized impurity, surface/interface roughness, electrolyte, and phonon scattering in degenerately doped semiconductors to fit the data in Figs. 4(a) and 4(b). As in Ref. 5, we quantify scattering from charged threading dislocations through

μdisl=8ea2πhNdis3nAπ2/31+ξ03/2,
(2)

where a = 4.116 Å is the lattice parameter, Ndisl is the average threading dislocation density (one elementary charge per unit cell is assumed), and ξ0 = εsε0h2(3π2nA)1/3/(me*e2). The constants e, h, ε0, me*, and εs are the electronic charge, Planck constant, vacuum permittivity, electron effective mass (∼0.2me4,5), and semiconductor relative permittivity (∼2053), respectively. Also following Ref. 5, ionized impurity scattering is quantified via

μii=3εs2ε02h3me*2z2e3nANii1FnA,
(3)

where F(nA) is a screening function,5,Nii is the ionized impurity concentration, and z is the impurity charge. In applying (2) and (3), we make the simplifying assumption that threading dislocations present one positive charge per unit cell such that Nii = Ndisl/a + n0. Dislocation-free films would thus have Nii = n0, i.e., we ignore, for now, other charged defects and compensation. Following Ref. 54, scattering due to BSO surface roughness, i.e., the BSO/ion gel interface roughness, is captured by

μroughness2.4lΔ2εsε0hπme*2en2D,
(4)

where n2D = nAdA is the 2D electron density in the accumulation layer, ∆ is the surface step height, and l is the correlation length.54 Scattering from the electrolyte ions at the BSO/ion gel interface is treated as discussed in Sec. C of the supplementary material, essentially considering cations in the EDL as surface dopants.55,56 This yields

μiongelC2πehεr+εs2ε0h2πme*e22,
(5)

where C ≈ 3 is a dimensionless constant deduced from comparison with prior experiments (see Sec. C and Fig. S4 of the supplementary material) and εr ≈ 12 is the relative permittivity of the ion gel.57 To fit the data in Fig. 4(a), at low T (2 K–50 K), where phonons can be neglected, we then use Matthiessen’s rule

μlowT=1μdisl+1μii+1μroughness+1μiongel1,
(6)

with only two free parameters: Ndisl and l/∆2. As expanded on below, however, surface/interface roughness scattering is only significant in the highest mobility films, where the extracted l/∆2 are essentially constant and in good agreement with the estimates from the structural characterization of representative films; this effectively reduces the number of free parameters to one (Ndisl).

The solid lines in Fig. 4(a) are fits to (6), demonstrating that the above equations well describe μA(nA). The extracted l/∆2 values, which are only relevant for the highest mobility films, are ∼39 nm−1–52 nm−1, in good agreement with an estimated 25 nm−1–50 nm−1 (∆ ≈ 0.2 nm, l ≈ 1 nm–2 nm) from high-resolution STEM on a LaAlO3(001)/LaxBa1−xSnO3 film (Fig. S3 of the supplementary material). In contrast, and more importantly, the extracted Ndisl varies widely, as shown in Table I and Fig. 4(c). In particular, as shown in Fig. 4(c), Ndisl decreases substantially as dtot (=dactive + dbuffer) increases, MBE-grown films generally having lower Ndisl. These findings are easily rationalized, as increased dactive and dbuffer are expected to lead to the gradual filtering of threading dislocations,10,14,17,29 while lower Ndisl in MBE films is generally consistent with superior mobility.11,14,15 Quantitatively, the extracted Ndisl for the LaAlO3(001)/BaSnO3 (114 nm)/LaxBa1−xSnO3 (29 nm) film is 1.3 × 1012 cm−2 (the lowest value obtained), consistent with the ∼1012 cm−2 deduced in prior work on similar films.14 The thinner, lower mobility films in Fig. 4(c) have extracted Ndisl values that exceed typical densities from STEM (∼1011 cm−2–1012 cm−215) by around an order of magnitude. This is also simply rationalized, as charged defects other than dislocations and ionized donors are not directly accounted for in Eqs. (2)–(6). Non-stoichiometry-related point defects,14 compensating defects,14 and 2D defects,15,28 which are known in BSO, are thus captured as increased Ndisl in our analysis.

TABLE I.

Sample description, growth method, active layer thickness (dactive), undoped buffer layer thickness (dbuffer), ionized impurity density (Nii), ionized impurity charge (z), and extracted threading dislocation density (Ndisl) for each film in this study. Nii is simply set to n0(300 K), which, as discussed in the text, ignores effects such as other charged defects, compensation, and freeze-out. For La-doped films, z was set at 1, and for VO-doped films, z was set at 2; the unintentionally doped GdScO3(001)/BaSnO3 film was assumed to be VO-doped.

SampleGrowth methoddactive (nm)dbuffer (nm)Nii (1019 cm−3)zNdisl (1012 cm−2)
LaAlO3(001)/BaSnO3/LaxBa1−xSnO3 (29 nm) MBE 29 114 3.5 1.3 
LaAlO3(001)/BaSnO3/LaxBa1−xSnO3 (30 nm) MBE 30 30 7.7 5.8 
GdScO3(001)/BaSnO3−δ (51 nm) MBE 51 ∼0 2.7 
LaAlO3(001)/BaSnO3−δ (54 nm) Sputtering 54 0.18 9.3 
LaAlO3(001)/LaxBa1−xSnO3 (51 nm) Sputtering 51 8.0 27.2 
LaAlO3(001)/BaSnO3−δ (12 nm) Sputtering 12 4.1 38.2 
LaAlO3(001)/BaSnO3−δ (10 nm) Sputtering 10 1.7 49.5 
SampleGrowth methoddactive (nm)dbuffer (nm)Nii (1019 cm−3)zNdisl (1012 cm−2)
LaAlO3(001)/BaSnO3/LaxBa1−xSnO3 (29 nm) MBE 29 114 3.5 1.3 
LaAlO3(001)/BaSnO3/LaxBa1−xSnO3 (30 nm) MBE 30 30 7.7 5.8 
GdScO3(001)/BaSnO3−δ (51 nm) MBE 51 ∼0 2.7 
LaAlO3(001)/BaSnO3−δ (54 nm) Sputtering 54 0.18 9.3 
LaAlO3(001)/LaxBa1−xSnO3 (51 nm) Sputtering 51 8.0 27.2 
LaAlO3(001)/BaSnO3−δ (12 nm) Sputtering 12 4.1 38.2 
LaAlO3(001)/BaSnO3−δ (10 nm) Sputtering 10 1.7 49.5 

Insight into the relative importance of dislocation, ionized impurity, roughness, and ion gel scattering is provided by the dotted lines in Fig. 4(a), which show the nA dependence of μdisl, μii, μroughness, and μion gel extracted from fits to the highest mobility LaAlO3(001)/BaSnO3 (114 nm)/LaxBa1−xSnO3 (29 nm) film. It is readily seen that the mobility is limited by threading dislocations and ionized impurities at low to moderate nA, but by ion-gel-induced scattering at nA above ∼1020 cm−3. The peak in μA(nA) thus arises from competition between improved screening of charged defects with increasing nA [Eqs. (2) and (3)] and the slowly decreasing μion gel with increasing nA in Eq. (5); the latter arises due to the increase in me* with nA (see Ref. 5). Interestingly, and consistent with Ref. 56, mobility in electrolyte-gated BSO would therefore likely be improved by insertion of an appropriate spacer layer at the BSO/ion gel interface. In SrTiO3/LaAlO3 two-dimensional electron systems, for example, insertion of ultrathin atomically smooth BN flakes improves the mobility by an order of magnitude while maintaining 1014 cm−2 carrier densities.58 We note that scattering due to surface/interface roughness is also likely to be a factor at very high nA, the nA dependence in Eq. (4) reflecting more frequent roughness scattering as the Fermi velocity increases in degenerately doped films.

Finally, modeling 300 K data [Fig. 4(b)] requires that we account for phonons. Following Ref. 5, this is done by quantifying scattering from longitudinal optical phonons through

μphonon1=i12ciωieme*1+ci63fci×ehωi2πkBT11,
(7)

where ci is the electron–phonon coupling constant for each phonon mode i, ωi is the phonon frequency (18 meV, 54 meV, and 91 meV modes are considered), kB is Boltzmann’s constant, and f(ci) is a dimensionless function.5 Equation (6) is then modified by adding a 1/μphonon term, resulting in the solid line fits in Fig. 4(b). The model again describes the data well, this time over an nA range from ∼1018 cm−3 to >1020 cm−3, i.e., more than two orders of magnitude. Examining the scattering from the various sources (colored dashed lines), phonons are seen to limit the mobility above ∼2 × 1019 cm−3 in LaAlO3(001)/BaSnO3 (114 nm)/LaxBa1−xSnO3 (29 nm), decreasing the peak μA by a factor of ∼2 compared to Fig. 4(a).

In summary, ion-gel-based solid electrolyte gating has been used to probe electron-density-dependent transport in sputtered and MBE-grown BaSnO3 with widely varied substrate, buffer layer structure, thickness, and initial chemical doping and mobility. In lightly chemically doped and undoped films, insulator–metal transitions can be gate induced, leading to mobility enhancement up to 2000%. In more heavily doped films, electrostatic electron accumulation also boosts mobility, self-consistent Schrödinger–Poisson and two-channel conduction modeling demonstrating 300 K mobility up to 140 cm2 V−1 s−1, comparable to the highest values reported in BaSnO3 films. A remarkably universal mobility–electron density relation is found, the mobility first increasing to ∼1020 cm−3, before decreasing at the highest gate-induced electron densities. Through analytical modeling accounting for charged threading dislocations, ionized impurities, surface/interface roughness, electrolyte, and phonon scattering, this non-monotonicity is shown to derive from a crossover from mobility limited by dislocation and ionized impurity scattering to electrolyte-limited mobility. These results significantly elucidate mobility limiting scattering mechanisms in BaSnO3, at the same time providing broadly relevant understanding of mobility peaks in electrolyte-gated materials.

See the supplementary material for further T- and Vg-dependent transport data on BSO films of various thicknesses, initial doping, and mobility; STEM characterization of surface roughness; and the derivation of Eq. (5).

C.L. and H.W. conceived this study. H.W. fabricated the EDLTs and performed transport measurements and analyses under the guidance of C.L. Sputter deposition and characterization was performed by H.W. and K.G. under the guidance of C.L. Molecular beam epitaxy was performed by A.P. under the guidance of B.J. K.R. developed the model for electrolyte scattering. H.W. and C.L. wrote the paper, with input from all authors.

The data that support the findings of this study are available within the article, its supplementary material, or from the corresponding author upon reasonable request.

This work was primarily supported by the National Science Foundation (NSF) through the University of Minnesota (UMN) MRSEC under Grant No. DMR-1420013. Parts of this work were carried out at the Characterization Facility, UMN, which receives partial support from the NSF through the MRSEC program. Portions of this work were also conducted at the Minnesota Nano Center, which is supported by the NSF through the National Nano Coordinated Infrastructure Network, under Grant No. NNCI-1542202. The authors acknowledge H. Yun for STEM imaging and B. Shklovskii for illuminating discussions.

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Supplementary Material