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A consistent picture of excitations in cubic BaSnO3
revealed by combining theory and experiment1234567890():,;

Wahib Aggoune 1,2 ✉, Alberto Eljarrat 1, Dmitrii Nabok1, Klaus Irmscher3, Martina Zupancic3,
Zbigniew Galazka3, Martin Albrecht 3, Christoph Koch1 & Claudia Draxl 1,2

Among the transparent conducting oxides, the perovskite barium stannate is most promisingfor various electronic applications due to its outstanding carrier mobility achieved at room
temperature. However, most of its important characteristics, such as band gaps, effective
masses, and absorption edge, remain controversial. Here, we provide a fully consistent picture by combining state-of-the-art ab initio methodology with forefront electron energy-loss
spectroscopy and optical absorption measurements. Valence electron energy-loss spectra,featuring signals originating from band gap transitions, are acquired on defect-free sample
regions of a BaSnO3 single crystal. These high-energy-resolution measurements are able tocapture also very weak excitations below the optical gap, attributed to indirect transitions. By
temperature-dependent optical absorption measurements, we assess band-gap renormalization effects induced by electron-phonon coupling. Overall, we ﬁnd for the effective electronic mass, the direct and the indirect gap, the optical gap, as well as the absorption onsets
and spectra, excellent agreement between both experimental techniques and the theoreticalmany-body results, supporting also the picture of a phonon-mediated mechanism
where indirect transitions are activated by phonon-induced symmetry lowering. This work
demonstrates a fruitful connection between different high-level theoretical and experimental
methods for exploring the characteristics of advanced materials.

1 Institut für Physik and IRIS Adlershof, Humboldt-Universität zu Berlin, 12489 Berlin, Germany. 2 Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195
Berlin, Germany. 3 Leibniz-Institut für Kristallzüchtung, 12489 Berlin, Germany. ✉email: aggoune@physik.hu-berlin.de

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ransparent conducting oxides (TCO) have attracted theattention of researchers and engineers due to their wide
range of potential applications. Among them, the perovskite
BaSnO3, when doped with lanthanum, has turned out as the mostpromising candidate for the next generation of electronic devices.
This is mainly due to the combination of extraordinary roomtemperature mobility, reaching 320 cm2 V−1 s−1—which is thehighest ever measured in TCOs—and a signiﬁcant degree oftransparency in the visible range1. Additionally, BaSnO3 exhibits
excellent thermal stability. As such, it is already explored as achannel material in ﬁeld-effect transistors and as an electrontransporting layer for highly efﬁcient dye-sensitized solar cells1–6.
The high mobility in this material is attributed to the low effective
electron mass of the conduction band, composed of Sn-s states, aswell as to the reduced carrier scattering due the large dielectric
constant3,7. However, at higher doping densities, it was shown thationized-impurity scattering may limit the mobility8. As an alternative to La-doping, an exciting perspective has been opened bypolar-discontinuity doping, i.e., by forming interfaces or heterostructures of the nonpolar BaSnO3 with a polar oxide perovskite.
In this case, a high-mobility two-dimensional electron gas can beformed in BaSnO3 without doping4,8–14.
Detailed knowledge of the pristine material is a prerequisite forthe fundamental understanding of its doped or nanostructured
counterparts and, consequently, for developing such promising
applications. In the past years, the electronic and optical properties of BaSnO3 have been intensively investigated from boththeory and experiment3,8,11,15–28. However, effective masses,
band gaps, and absorption edges are still controversial. While thevalue of the fundamental gap is under debate, there is evidence of
its indirect character, obtained by angle-resolved photoemission
spectroscopy29 and absorption measurements22. Measured
values3,15–18,20–24 for the indirect fundamental gap vary between
2.85 and 3.3 eV, while for the direct counterpart between 3.1 and
4 eV, with a majority of the latter being around 3.5 eV. The
corresponding estimates of the difference between the two range
between 0.15 and 0.5 eV. These diverse ﬁndings were assigned tothe presence of uncontrolled defects as well as to differences inmeasurement techniques. Also, the experimental estimates of theeffective electron mass are scattered, ranging between 0.19 and0.65 m03,7,20,24,30.
From the theoretical side, density-functional-theory (DFT)
calculations based on semi-local exchange–correlation (xc)functionals31 ﬁnd an indirect fundamental gap that is underestimated by about 75%. Incorporating 25% of Hartree–Fockexchange, the hybrid functional HSE0632 naturally improves
the results. The still too small gap (by about 15%) was explainedby the signiﬁcant dielectric screening included in thefunctional8,11,25–27. The calculated electron masses also widely
scatter between 0.06 m0 and 0.9 m0, depending on the xc
treatment20,27.
Absorption measurements show a weak signal at the onset3,
suggesting it to be related to the indirect gap. This was later
conﬁrmed22, and a temperature-induced shift of about −0.18 eV
was reported, going from 5 to 297 K. In addition, a recent theoretical study28 reveals phonon-assisted absorption across theindirect gap, also leading to the temperature dependence of thespectrum.
For an in-depth understanding of this puzzle, several parametersneed to be disentangled: These are the values of the fundamental
direct and indirect gaps, the impact of electron–phonon (e-ph)coupling in terms of zero-point vibrations (ZPV) and temperature,
as well as electron–hole (e–h) interaction (exciton-binding energies)
for direct as well as indirect transitions. To this end, we present a
combined theoretical and experimental study of the electronic
structure and the optical excitations of cubic BaSnO3.
2

Our theoretical analysis is based on many-body perturbation
theory (MBPT) in the framework of the G0W0 approximation33,34
and the Bethe–Salpeter equation (BSE)35–37. To understand therole of xc effects on the electronic structure, we ﬁrst compute the
DFT band structure, employing both semi-local and hybrid xc
functionals. Then, we obtain the quasi-particle (QP) bands
by self-energy corrections. Through a detailed analysis of thedielectric function, we discuss the impact of e-h interaction on theabsorption edge. We present the origin and the spatial distribution of the e-h pairs that dominate the different frequency ranges.
Furthermore, we discuss the impact of e-ph coupling on the optoelectronic excitations at the onset.
The theoretical absorption spectrum is compared with electronenergy loss spectroscopy (EELS) performed on a single crystal.
Here we succeed in using EELS at high-energy resolution as astand-alone technique for measuring the band gap as well as
obtaining the dielectric function of BaSnO3. An advantage of thisset-up is that transmitted electrons interact more strongly withmatter than photons, transferring momentum to the orbital electrons, which enhances the measurability of indirect band gaps38.
Moreover, it can be performed on a small crystal volume. In thisway, one can select defect-free sample regions, offering the possibility to assess the properties of the perfect crystal. However, theobservation of band gaps and other electronic features by EELS istypically hampered by spurious contributions from the surface andrelativistic losses. Also for this particular material, the relatively
high refractive index at the energy region close to the band gap
indicates that relativistic losses contribute to the spectrum ofelectrons transmitted with accelerating voltages >60 kV. Purely
experimental procedures have been proposed to generally address
this issue, including low-voltage and off-axis EELS39,40. Nevertheless, these procedures are material speciﬁc and can make theanalysis of the spectra difﬁcult41,42. Recently, inverse algorithms
based on modiﬁed Kramers–Kronig analysis (KKA) are emerging
as an advantageous alternative to purely experimental methods43.
In this off-line approach, a self-consistent estimate of the spurious
contributions to the EELS spectra is obtained and removed fromthe experimental data. Here we demonstrate how this technique
can be applied to reveal previously unknown valence properties
and obtain a measurement of the dielectric function. With
these measurement techniques, onsets of both direct and indirecttransitions can be captured. To examine the possible role ofindirect interband transitions on the absorption onset, the spectrum is also computed and analyzed at ﬁnite momentum transfer.
Through temperature-dependent optical absorption measurementsof the optical onset, we determine to which extent e-ph coupling
renormalizes the band gap, complementing the quantitative comparison between theory and experiment to give a fully consistentpicture.
Results and discussion
Electronic structure. At room temperature, BaSnO3 crystallizes
in the cubic perovskite structure with space group Pm3m asshown in Fig. 1. Its primitive unit cell containing ﬁve atoms
exhibits a highly symmetric (non-tilted) SnO6 octahedra. The
lattice constant of 4.127 Å obtained with the PBEsol functional isclose to the experimental value of 4.116 Å1. As the band gap of
this material is very sensitive to strain44, we adopt the latter in thefollowing calculations to ensure a quantitative comparison
between measured and computed quantities. Considering theformal ionic charges of Ba (+2), Sn (+4), and O (−2), BaSnO3 isformed by alternating neutral BaO and SnO2 layers along the[100], [010], and [001] directions, making it a nonpolar material.
We ﬁrst present the electronic band structure obtained by
PBEsol and HSE06. The corresponding values of the band gaps

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Table 1 Band gaps, Eg, and effective electron masses, me /m0, of cubic BaSnO3, obtained by PBEsol, HSE06,
G0W0@PBEsol, and G0W0@HSE06.

Eg [eV]me /m0

Fig. 1 Crystal structure of cubic BaSnO3. Primitive cell (a) and ﬁrst
Brillouin zone (b) with high-symmetry points and paths (red) as used inFig. 2.

are reported in Table 1. The results for PBEsol shown in Fig. 2a,
indicate an indirect band gap of 0.9 eV, with the valence-band
maximum (VBM) and the conduction-band minimum (CBm)located at the R and the Γ point of the Brillouin zone, respectively.
The direct gap, located at Γ, is about 1.39 eV. These values
underestimate the experimental counterparts by about 70%. As
shown in the middle panels of the ﬁgure, the VBM is mainly
dominated by O-p states, while the highly dispersed conduction
band around Γ exhibits mainly Sn-s character with some
contribution from O-s orbitals (see Figs. 2a and 3). Ba-d states
dominate the conduction bands between 5 and 9 eV, while Ba-fderived bands appear above 9 eV. At the R point, the VBM and
CBm are threefold degenerate, exhibiting O-p and Ba-d character,
respectively (see also Fig. 3b). In addition, the CBm has some
contribution from Sn-p states. At the Γ point, the VBM is also
threefold degenerate, showing O-p character. The PBEsol band
structure including spin–orbit coupling is shown in the rightpanel of Fig. 2a. The effect of spin–orbit coupling is small within
the energy range between −9 and 12 eV, in agreement with aprevious theoretical study45. Pronounced spin–orbit coupling
appears in the valence band at about −10 eV, where the Ba-pbands split by about 1.80 eV. Since these strongly affected bands
do not enter the calculation of the optical properties, spin–orbit
coupling is neglected in the following. We also note that there is
no change in the size of the indirect or direct band gap due tospin–orbit coupling.
Employing the hybrid functional HSE06, the indirect (direct)
band gap increases to 2.70 (3.13) eV (see Table 1). These values
that are in agreement with previous theoretical values25 still
underestimate the experimental values by about 10%. Besides, we
notice several changes in the band structure upon using HSE06.
As evident from the left panel of Fig. 2b, conduction bands can beapproximated by a simple scissor shift with respect to those given
by PBEsol up to 10 eV above the CBm. For the bands lying above,the scissor approximation is not valid due to changes in the band
dispersion as well as the band order caused by the localized
nature of Ba-d and -f states. As an example, the Ba-f-derived
bands at about 12 eV in the PBEsol band structure are shifted up
by about 3 eV in HSE06.
To obtain the QP band structure, we apply a self-energy
correction (Eq. (3)) in the G0W0 approximation. To this end, we
consider both the PBEsol and the HSE06 band structure as astarting point, and the results are depicted in the middle and rightpanel of Fig. 2b, respectively. As shown in Table 1, the QP
correction increases the indirect (direct) gap by approximately
1.7 eV, resulting in 2.62 (3.08) eV. Such a large magnitude of theself-energy correction reﬂects the strong electron-electron
correlation effects in this material. Therefore, a pronounced
starting-point dependence is expected. The QP gaps obtained
starting from PBEsol are close to those of plain HSE06. G0W0 on

R–Γ
Γ–Γ
Γ–X

DFT

DFT

G0W0@

G0W0@

PBEsol

HSE06

PBEsol

HSE06

0.90
1.39
0.17

2.70
3.13
0.21

2.62
3.08
0.20

3.50
3.96
0.20

top of the latter (G0W0@HSE06) leads to a further increase by
about 0.8 eV, giving values of 3.50 (3.96) eV for the indirect(direct) gap. This method has turned out most reliable forcomputing the electronic properties of a wide range of oxides,
including TCOs46. However, as expected, these values are larger
than most experimental gaps as neither ZPV nor temperatureeffects are considered here. We will get back to this point in thesection “Optical properties”.
Looking at the entire band structures, the QP correction toboth PBEsol and HSE06 varies from band to band and depends
on the k-point, speciﬁcally, within the bands where the localized
Ba-d and Ba-f states appear. The bands derived from the latter(not shown) are located about 14 eV above the CBm in both
G0W0@PBEsol and G0W0@HSE06 (see Fig. 2b). Overall, a simple
scissor shift of the DFT conduction bands is sufﬁcient to capture
the features of the unoccupied bands up to 10 eV above the CBm.
However, for computing optical spectra in a larger energy
window (>10 eV), the QP band structure is needed23. Due to thecomputational complexity, we use the QP band structure
obtained by G0W0@PBEsol and a scissors operator of 0.88 eV
to recover the G0W0@HSE06 band gap.
Finally, we focus on the effective electron masses for which
previous calculations have shown that it is sensitive to the xc
functional20,27. Our results are summarized in Table 1. For visualinspection, we plot in Fig. 3a all band structures computed in thiswork in the vicinity of the band gap, setting the CBms to zero.
Although there exists a dependency on the applied method, thedifferences stay within approximately 15%. While PBEsol and
HSE06 calculations give about 0.21 and 0.17 m0, respectively,
along the Γ–X direction, and the same values are found also
along the Γ–M and Γ–R directions, we obtain 0.20 m0 withboth G0W0@PBEsol and G0W0@HSE06. Compared with previous
calculations, our results are close to those obtained by
HSE068,11,25.
Optical properties. We proceed with our analysis by investigating the optical properties of BaSnO3. Previous investigations
reported the material to be transparent in the visible region andabsorbing light from the near-ultraviolet range above 3 eV, withrelatively low intensity, followed by intense absorption startingfrom 7 eV3,18,23,28,31. Difﬁculties to analyze the shape of theexperimental absorption edge arise mainly due to the fact that theabsorption onset originates from weak phonon-assisted transitions across the indirect band gap3,22,28. Further complications
arise from the presence of defects and impurities18. EELS
experiments in the scanning transmission electron microscope(STEM-EELS) turn out to be an advantageous experimental
technique to address these difﬁculties. One reason already mentioned is that momentum exchange increases the relevance of
indirect transitions. Additionally, when performed in the STEMEELS mode, properties from relatively small volumes of material
can be measured. This makes EELS desirable when larger defectfree samples are difﬁcult to obtain. To get insight into the

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Fig. 2 Band structure of cubic BaSnO3. a Result of PBEsol, where in the middle panel the band characters are highlighted; in the right panel, the effect ofspin–orbit coupling, SOC, is shown. b From left to right: comparison of HSE06 with PBEsol; G0W0@PBEsol; G0W0@HSE06. The valence band maximum is
set to zero.

characteristics of the absorption onset, we present and analyze inthe following computed and measured absorption spectra.
BSE calculations. In Fig. 4a, we depict the optical spectra of
BaSnO3 computed by the BSE. In the displayed energy range, we
identify two main regions, distinguished by their intensity.
Between 3.86 and 7 eV (region I), the absorption is relatively low.
Above that (region II), the intensity increases and a pronounced
peak centered at about 8 eV is formed. The e-h interaction vastly
redshifts the entire spectrum as observed from comparison with
the independent particle spectrum. The absorption starts at
3.86 eV (optical gap), which is 100 meV below the direct gap(3.96 eV) where the independent particle onset sets in. Region I
is governed by transitions between the O-p-derived valencebands and the Sn-s-derived conduction band. Bound excitons
give rise to high spectral intensity in the region around the direct
band gap. The lowest bound state, exciton A, arises from transitions around the VBM and the CBm at the Γ point of theBrillouin zone as highlighted in Fig. 4b. The corresponding e-h
wavefunction is shown in Fig. 4d for a ﬁxed hole position at theoxygen site. The electron is delocalized around the hole with athree-dimensional extension >20 Å, mainly spreading over the
Sn-s and the O-s orbitals. This delocalized character reﬂects therather low exciton binding energy of about 100 meV, which iscomparable to values in other oxides, e.g., in ZnO47 and
LaInO348.
Starting from 7 eV (region II), the spectral weight increases
steeply, where the peak at around 8 eV stems from intensive
transitions between O-p and Ba-d states. From the comparison
4with the corresponding peak in the independent particle
spectrum, one can notice a signiﬁcant red-shift by ~2 eV, inducedby e-h attraction (Fig. 4a) while local-ﬁeld effects are negligible.
Exemplary, we consider excitation B that contributes to the peak.
As evident from Fig. 4b, B is built of transitions between the VBM
and the CBm at the R point (see also Fig. 3b). The corresponding
excitonic wavefunction is characterized by a rather localized
electronic distribution (2–3 unit cells) surrounding the holewhose position is ﬁxed on an O atom for visualization (Fig. 4c).
The electrons spread mainly over Ba-d and to less extent overSn-s orbitals.
EELS measurements. In Fig. 4a, we also display the imaginary partof the dielectric function obtained by applying relativistic KKA(rKKA) to the EELS measurement. One can see excellent agreement with the BSE result in terms of peak positions, magnitude,
and overall shape. The real part of the obtained dielectric function(not shown) indicates that the threshold for Cherenkov radiationis considerably surpassed only for the energy region above theband gap, i.e., ~5–10 eV. In fact, our result indicates that the
impact of relativistic losses for the band-gap region is small,considering the experimental parameters and estimated thicknessof this sample. For more details and comparison between theory
and experiment of both real part and imaginary part at higher
energies, we refer the reader to Supplementary Fig. 3. Focusing on
the location of the absorption onset, we note that even after
plasma cleaning (see “Methods” section), there is still some weaksignal seen at about 2 eV (Fig. 4a). This might be mainly attributed to the remaining contamination at the BaSnO3 surface, but it

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Fig. 3 Electronic structure of BaSnO3. a Conduction band obtained by
PBEsol, HSE06, G0W0@PBEsol, and G0W0@HSE06. The conduction-band
minimum is set to zero. The inset zooms into the region of the CBm alongthe Γ–X direction. b Square modulus of the electronic Kohn–Shamwavefunction (yellow) of the valence-band maximum at R (a similar
distribution is found at Γ) as well as the CBm at Γ and R.

apparently does not affect the spectrum at higher energies.
Therefore, as depicted in Fig. 5a, we analyze the onset of the EELS
spectrum in order to understand the characteristic of theabsorption edge.
At ﬁrst glance, we recognize two regimes, consisting of a region
between 3 and ~3.5 eV where the signal only increases weakly,
followed by a drastically increasing intensity above 3.5 eV. Whilethe latter stems from strong direct transitions, we attribute theformer to originate from indirect transitions. This characteristic is
in line with recent experimental observations from opticalabsorption22, as well as with angle-resolved photoemission
spectroscopy29. This ﬁnding is also supported by calculations
on the independent particle level28.
To determine the absorption from the EELS spectra, we
employ the model introduced in the section “Methods,”
restricting the ﬁt to the energy range between 2.5 to 4.5 eV(see Supplementary Methods for more details). The model
parameters are adjusted using bounded optimization with theLevenberg–Marquart algorithm followed by dual annealing as
implemented in the Python package HyperSpy49. Our results
indicate that the onset of the indirect and direct transitions are at
2.97 ± 0.04 and 3.57 ± 0.04 eV, respectively. The difference
between the two onsets of about 0.60 ± 0.06 eV agrees well withthe calculated G0W0@HSE06 counterpart of ~0.45 eV (Table 1).
As shown in Table 2, excellent agreement is found with theoptical measurement of ref. 22. Overall, the measured values arealso in agreement with most reported experimental values thatare about ~3.019,23,24 and 3.5 eV18,19,21,29 for the onset of theindirect and direct transitions, respectively. Note that both values
are not fundamental band gaps as the spectra include excitonic
effects. A detailed comparison between experiment and theory
will be given in the last part before conclusions.

Fig. 4 Optical absorption of cubic BaSnO3. a Imaginary part of themacroscopic dielectric function obtained from the Bethe–Salpeter equation(BSE), which includes excitonic effects (solid line). The independent
quasiparticle spectrum (IQPA), is shown for comparison. A Lorentzianbroadening of 0.15 eV is applied to both spectra to mimic excitation
lifetimes. The experimental result (magenta circles) is obtained by applying
relativistic Kramers–Kronig analysis (rKKA) to electron energy-loss
spectroscopy (EELS) data. b Band contributions to excitations (A) and (B)marked in the BSE spectrum. c, d Spatial distribution of the electron–holewavefunction for excitations (A) and (B), with the hole ﬁxed on the O atom(yellow spots). In d, we also show the three-dimensional electron
distribution of excitation A, where only a few atomic layers of the BaSnO3
structure are shown to ease the visualization.

We also estimate the effective electron mass from the dielectric
function in the framework of the free-electron approximation50,!2
neff e_
ð1Þ
m ¼;
ε0 ε1 Epl
where neff is the effective valence electron density, ε∞ is thehigh-frequency dielectric constant, and Epl is the plasmonenergy of the material. The latter is retrieved as the zerocrossing of the real part from the negative half-plane (seeSupplementary Fig. 3). The obtained value of Epl ~ 25.2 eV is inexcellent agreement with the free-electron prediction for thismaterial using the experimental lattice parameter of 4.116 Å.

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Fig. 6 Temperature dependence of the absorption onset obtained by
optical-absorption measurements. The circles represent the measured
data; the corresponding solid line is the best ﬁt based on a single-oscillator
model. The dashed line shows a linear ﬁt for high temperatures. The inset
zooms into the low-temperature region to distinguish between gap
renormalization due to temperature (T-effect) and zero-point
vibrations (ZPV).

Fig. 5 Comparison between theory and experiment. a Electron energy-loss
spectroscopy (EELS) measurement (black solid line) of a BaSnO3 single
crystal in the energy range around the absorption onset. The ﬁts obtainedby a model assuming either indirect or direct transitions (see “Methods”
section) are shown by the red and blue dashed lines, respectively. The
dashed black line refers to the background model while the green solid line
shows the sum of the three models. The vertical blue line indicates theonset of direct transitions and the dashed red line that of indirecttransitions; the shaded areas represent their error bar. b Dielectric functionin the energy range of the absorption onset given by Bethe–Salpeter
equation (BSE, black solid line) and determined from EELS measurement(magenta circles). The intensity of the BSE spectrum for momentum
transfer q = q(ΓR) = (1/2,1/2,1/2), shown by the dashed line, is scaled by afactor of 50 for better visibility. A Lorentzian broadening of 0.2 eV isapplied. The blue line indicates the ﬁrst direct excitation (optical gap)
obtained for q0 = (0,0,0) (A), the red arrow refers to the ﬁrst indirecttransition for q = qΓR (A′). Both BSE spectra are corrected by a value of−0.367 eV to account for band-gap renormalization due to zero-point
vibrations and temperature.

Table 2 Absorption onset, Eonset, given by the energy of theﬁrst indirect transition, and optical gap, Eopt
g , determined by
the ﬁrst direct excitation, as obtained by the EELS and
optical absorption measurements22.
Experiment

Eonset [eV]

Eoptg [eV]EELS at 300 K
Optical absorption at 5 K
Optical absorption at 300 K

2.97 ± 0.04
3.17 ± 0.04
2.99 ± 0.04

3.57 ± 0.04——

6

The high-frequency dielectric constant obtained from the rKKA
analysis is ε∞ ~ 4.2, leading to an estimate for the effective
electron mass of m* ~ 0.16 m0. This value is very close to the
PBEsol result of ~0.17m0 and slightly lower but still comparable
to the G0W0@HSE06 value of 0.20 m0. The deviation could
be due to the usage of the simple free-electron framework.
Overall, these values conﬁrm experimental works reporting a
low effective mass of ~0.19 m07,30, which suggests high electron
mobility in BaSnO3.
Optical absorption. For a quantitative evaluation of band gaps andabsorption onsets, vibrational effects must be considered. Previous ﬁnite-temperature calculations28 indicate that the onset of
the indirect transitions at 300 K is about 0.19 eV below that at
0 K. The experimental counterpart was estimated to be about
0.18 eV (Table 2)22. In both cases, the role of ZPV was notknown. To remedy this situation, we perform optical absorption
measurements below room temperature. The resulting dependence of the energy onset is shown in Fig. 6. More information
related to the optical absorption spectra, crystal growth, andsample preparation can be found in ref. 22.
The measured data are ﬁtted using a single-oscillator model51,
expressed by




h_ωi
onset
onset
E
1 ;
ð2Þ
ðT Þ ¼ E
ð0Þ  Sh_ωi coth
2kB T
where the parameter Eonset(0) is the energy onset at zerotemperature, S is a measure of the e-ph coupling strength, and〈_ω〉 an average phonon energy48,51,52. Considering the wholetemperature range, the best-ﬁt parameters Eonset(0) = 3.17 eV,S = 6.5, and _ω = 28 meV are obtained. Extrapolating to 1200 K,
the energy is about 1 eV lower than at room temperature,
reﬂecting the strong impact of e-ph coupling. Similar values havealso been reported for other TCOs, such as In2O3 andSrTiO352,53. The high-temperature part of the curve can be ﬁtted
with linear regression, i.e., Eonset(0) − 2SkBT + S〈_ω〉51. The ZPV
contribution is, thus, given by S〈_ω〉, which amounts to 0.182 eV.
Going from 0 and 300 K, the onset decreases by about 0.367 eV,

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Table 3 Indirect QP gap, EQP
g , as given by G0W0@HSE06 at
0 K and optical gap, Eopt
g , obtained by the BSE [in eV].
Theory

EQP
g

-corr
EQP
g

EA

EA -corr

Eoptg

Egopt-corr

0K
300 K

3.50

3.32
3.13

3.40

3.22 (3.17)
3.03 (~3.0)

3.86

3.68
3.50 (3.57)

00

In addition to the energy of the ﬁrst direct excitation (A), deﬁning the optical gap, also the0energy of the ﬁrst indirect excitation (EA ) is provided. The corresponding values including
corrections (marked with “-corr") to account for ZPV and temperature effects, estimatedexperimentally, are depicted as well. For comparison, the related experimental gap values(Table 2) are given in brackets.

where 0.182 eV is assigned to ZPV and 0.185 eV to temperatureeffects, including lattice expansion. These values are comparable
to those reported for other TCOs48,52. These values will be used
as corrections to enhance the theoretical spectra as shown in
Fig. 5b.
Comparison between theory and experiment. The BSE spectrum
shown in Fig. 4a is formed only by vertical excitations. To
describe transitions across the indirect gap, i.e., from R to Γ, we
solve the BSE for momentum transfer qΓR = (1/2,1/2,1/2). Bothspectra are depicted in Fig. 5b, where the correction to accountfor vibrational effects, estimated above, is included in the scissors
shift (see “Methods” section).
We note that the latter spectrum has almost zero intensity at
the onset, compared to that of q0. This is attributed to the use of
the centrosymmetric BaSnO3 structure, i.e., we do not consider
atomic displacements due to phonons. As such, transitions
between the threefold degenerate VBM at the R point and the
CBm at the Γ point belonging to the T2u and A1g representationsof point group Oh, respectively, are dipole forbidden. However,mediated by vibrations, such transitions become opticallyallowed, as supported by calculations on the independent particle
level28. Therefore, we attribute the measured weak absorption
across the indirect band gap here (Fig. 5a) and in ref. 22 to thefact that phonons lower the symmetry of the here simulated
ideal crystal. Such effect has previously been observed inother materials54–56. Importantly, our BSE calculation at ﬁnite
momentum allows us to access the location of the ﬁrst indirecttransition as well as the amount of the excitonic effects. We notethat the differences between the rKKA-EELS and the BSE (q = 0)
spectrum in Fig. 5b are mainly due to ignoring temperature in thelatter, which has been reported to reduce the intensity at theonset28.
In Table 3, we report the indirect QP gap, as given by
G0W0@HSE06 at 0 K, and the optical gap obtained by the BSE.
The latter is given by the ﬁrst direct excitation (A) (Fig. 5b). In
addition, we also provide the energy of the ﬁrst indirect excitation(A’). The corrected values, accounting for ZPV and temperatureeffects shown in Fig. 6, are also shown. At room temperature, thefundamental QP gap is 3.13 eV. We obtain the absorption onset(excitation A’) and the optical gap (excitation A) at room
temperature to be 3.03 and 3.5 eV, respectively. The former is inexcellent agreement with both EELS (2.97 ± 0.04 eV) and opticalabsorption (2.99 ± 0.04 eV) counterparts (Fig. 5). The latter value
is also in very good agreement with the optical gap obtained by
the EELS measurement (3.57 ± 0.04 eV; see Fig. 5).
Finally, the binding energy of excitation A’ amounts to
100 meV, the same value as that of the direct excitation A (seeFig. 5b). We note that the excitonic effect in the EELS
measurement may be smeared out at room temperature. Anyway,
the predicted, relatively small computed value is within theexperimental error bar. Considering the measured absorption
onset at 3.0 eV, we can deduce the fundamental gap by adding theexcitonic binding energy. Doing so, we arrive at a value of
Eexp
g =3.1 eV at room temperature.
Conclusions
We have presented a detailed analysis of the electronic and opticalproperties of the cubic perovskite BaSnO3 from a ﬁrst-principles,many-body study, and experiment. Applying a self-energy correction to the bands obtained by the hybrid functional HSE06(G0W0@HSE06), we predict an indirect (direct) QP gap of 3.50
(3.96) eV and an effective electron mass of about 0.2 m0.
Spin–orbit coupling has a minor effect on the band edges. The
optical gap obtained by BSE calculations is 3.86 eV (not considering vibrational effects), reﬂecting an exciton binding energyof 100 meV of the lowest-energy excitation. The latter has adelocalized character, distributed over Sn-s and O-s orbitals.
Above 7 eV, Ba-d states are involved in the transitions and giverise to more localized excitons with high binding energy.
Temperature-dependent optical absorption measurements
show the optical onset to decrease by about 0.185 eV going from 5
to 300 K. Below that, ZPV effects are estimated to amount to afurther reduction of 0.182 eV. Including the latter corrections, theBSE spectrum shows an excellent agreement with the experimental counterpart obtained from the EELS measurement, in
terms of energy, intensity, and shape. The latter captures anadditional weak absorption feature below the strong direct transitions. It is assigned to indirect transitions driven by phonons, asreported previously in a theoretical work28. The onset of directtransitions (optical gap) is observed at 3.57 ± 0.04 eV, in good
agreement with the theoretical value of 3.50 eV. The calculated
spectrum at ﬁnite momentum transfer shows that the lowest
excitation across the indirect gap has also binding energy of about
100 meV. It sets in at about 3.03 eV, in excellent agreement with
its counterparts obtained by EELS (2.97 ± 0.04 eV) and by opticalabsorption (2.99 ± 0.04 eV). As such, indirect excitations are
dipole forbidden and thus should not be observed in the latter
experiment for a perfect crystal, and our ﬁndings support thetheoretical observation28 of the weak absorption across theindirect gap to be related to phonon-induced symmetry lowering.
Overall, we have demonstrated that the combination of stateof-the-art techniques in both theory and experiment and carefulanalysis allows for quantitative characterization of excitations in
crystalline materials as exempliﬁed by BaSnO3.
Methods
First-principles calculations. Ground-state (GS) properties are calculated using
DFT57,58 with the generalized gradient approximation in the PBEsolparameterization59 for the xc functional. Also, the hybrid functional HSE0632 with
25% of Hartree–Fock exchange is employed to compute the electronic properties.
QP energies are obtained by the G0W0 approximation33,34 by solving the QP
equation
QP
KS
KS KS
ϵQP
¼ ϵKS
i
i þ hϕi jΣðϵi Þ  vXC jϕi i;ð3ÞKS
where Σ is the non-local and energy-dependent electronic self-energy, ϵKSi and ϕiare the Kohn–Sham energies and wave-functions, respectively. Band structure andeffective masses are computed by making use of the Wannier interpolation60.
The optical spectra are obtained by solving the BSE, the equation of motion of
the two-particle Green function35–37. This problem can be mapped onto the secularequationλλ λ∑ H BSE
vck;v0 c0 k 0 Av0 c0 k 0 ¼ E Avck;v 0 c0 k 0

ð4Þ

where v, c, and k indicate valence bands, conduction bands, and k-points in thereciprocal space, respectively. The effective Hamiltonian consists of three terms,
HBSE = Hdiag + Hdir + 2Hx. The ﬁrst term, Hdiag, accounts for vertical transitions
between QP energies and, when considered alone, corresponds to the independent
quasiparticle approximation (IQPA). The other two terms incorporate the screened
Coulomb interaction (Hdir) and the bare e-h exchange (Hx). The factor 2 in front of
the latter accounts for the spin multiplicity in non-spin-polarized systems. The
eigenvalues of Eq. (4), Eλ, are the excitation energies. The corresponding
eigenvectors, Aλvck , provide information about the composition of the λ-th

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excitation and act as weighting factors in the transition coefﬁcients
hvkjb
pjcki
tλ ¼ ∑ Aλvck;
ϵck  ϵvkvck

ð5Þthat determine the oscillator strength in the imaginary part of the macroscopic
dielectric function,
ImεM ¼8π 2∑ jt j2 δðω  Eλ Þ;
Ω λ λ

ð6Þ

where Ω is the unit cell volume.
All calculations are performed using exciting61–63, an all-electron fullpotential code, implementing the family of linearized augmented planewave plus
local orbitals ((L)APW+LOs) methods. The atomic radii are chosen 2.2 bohr for
Ba, 2.0 bohr for Sn, and 1.6 bohr for O. The local part of the LAPW basis includes
three s, p, and d local orbitals for Ba and Sn and three s and p local orbitals for O.
The Sn 4s and 4p orbitals are treated as semicore states. The LAPW cutoff Gmax is
set to 5.0 bohr−1, which guarantees adequate convergence of the GS properties.
Spin–orbit coupling is included by the use of a second-variational procedure.
Brillouin zone integrations are carried out on an 8 × 8 × 8 k-grid for all total-energy
and electronic-structure calculations. In the HSE06 calculations, a basis-set cutoff
Gmax = 4.375 bohr−1 and 250 unoccupied states are used. The G0W0 QP band
structures is computed using as a starting point either PBEsol or HSE06 eigenstates.
Here, the same computational parameters are chosen as for HSE06, reaching a
numerical precision of about 30 meV for the band gap (see Supplementary Fig. 1).
The frequency-dependent screened Coulomb potential is treated in the randomphase approximation and computed on a grid of 16 imaginary frequencies. Padé
approximation is employed for evaluating the self-energy on a real frequency meshto solve the QP Eq. (3).
For the solution of the BSE63 on top of the QP band structure, an LAPW cutoff
Gmax of 4.375 bohr−1 is employed. The screened Coulomb potential is computed
using 100 empty bands. In the construction and diagonalization of the BSE
Hamiltonian, 9 occupied and 7 unoccupied bands are included, and a
14 × 14 × 14 shifted k-point mesh is adopted. Owing to the high dispersion of the
conduction band around its minimum at the Γ point, the k-point sampling isinterpolated onto a 28 × 28 × 28 mesh, using a double grid technique64. These
parameters ensure well-converged spectra within an energy window up to 10 eV,
and precision of the binding energy of the lowest-energy exciton within 20 meV(see Supplementary Fig. 2). For the q-dependent absorption spectra63, we solve the
BSE for a momentum transfer of q(ΓR) between Γ and R using the centrosymmetricstructure (i.e., without considering atomic displacement due to phonons). Since wefocus on the absorption onset, it is sufﬁcient to use the PBEsol band structure andapply a scissor operator. In this case, three occupied and two unoccupied bands areincluded for the construction and diagonalization of the BSE Hamiltonian, and a
20 × 20 × 20 shifted k-point mesh is adopted. This parameter choice ensuresconverged spectra up to 5 eV, and a numerical uncertainty of <10 meV for thebinding energy of the lowest-energy excitons. We note that the point groupsymmetry analysis was carried out by using the Irvsp tool65 of the VASP code.
We note that we also computed the electronic and optical properties of BaSnO3
using the optimized lattice parameter of 4.127 Å. The main difference with theresults presented in this work is found in the size of the band gaps (direct andindirect) which are about 0.12 eV smaller than those reported here. Atomic
structures and isosurfaces are visualized using the software package VESTA66.
EELS measurements. Plan-view transmission electron microscopy (TEM) samples
oriented along the [100] lattice direction of the BaSnO3 single crystal are preparedby classical tripod polishing, i.e., the same technique and growth conditions asreported in ref. 22. Additional smoothing of the surface is obtained by chemicalmechanical polishing (CMP) using the SiO2 suspension. Argon ion-milling is done
at liquid nitrogen temperature using a Precision Ion Polishing System (PIPS) at
beam energies of 3.5–0.2 keV.
STEM-EELS are carried out using a Nion HERMES microscope. This
instrument is equipped with an aberration corrector, a cold-ﬁeld emission gun, amonochromator at ground potential, and a hybrid-pixel direct-detection camera(Dectris ELA). Such experimental set-up allows one to acquire EELS spectra withenergy resolution below 10 meV at 60 kV accelerating voltage. In our case, we use
relatively large energy dispersions of 5, 50, and 100 meV/channel and opt for
opening the monochromatic slit to allow for more intensity in the beam at theexpense of some energy resolution. Using the smallest dispersion and 10 mrad
convergence and collection angles, we measure a zero-loss peak with the full widthhalf maximum (ZLP-FWHM) in the vacuum of ~40 meV (see Supplementary
Fig. 6). We monitor the relative alignment of the electron beam and crystalline
plane orientation, acquiring spectra using on-axis and off-axis conditions (seeSupplementary Fig. 4). The on-axis spectra are better suited for the study of thedielectric function using KKA. The off-axis spectra show better statistics and also
reproduce well the shape of the signal in the region of the optical gap (Eoptg ). Finally,
only the on-axis spectrum is presented here, but both can be found in
Supplementary Fig. 5.
In addition to these measurements, the impact of thickness and surface
contamination is studied. On the one hand, we initially ﬁnd no difference in theapparent optical gap for spectra acquired at thicker or thinner regions. The
8

consistency of these measurements is achieved due to the use of a relatively low
beam voltage of 60 kV in our STEM experiments. On the other hand, we ﬁndindications that surface contamination, originating from sample preparation andubiquitous hydrocarbons from the atmosphere, strongly affects our ability toobserve a signal from indirect transitions. Thus, the ﬁnal measurements reported
here are performed after the sample is treated using plasma cleaning with Argon.
The STEM-EELS characterization of BaSnO3 is carried out with the objective of
measuring low-loss EELS spectra. In this technique, inelastically scattered electrons
with energy loss in the range from zero up to a few tens of eV provide analternative means of studying the dielectric properties of thin samples. In contrast
to photons, the strongly interacting electrons allow for studying direct and indirecttransitions. In particular, the position of the onset of the inelastic signal at a few-eV
in a semiconductor material is related to its optical onset.
Naked-eye examination of these spectra already hints at the presence of the
optical gap at around 3 eV. Indeed, for our experimental set-up, at this energy
resolution and owing to the use of a direct-detection camera, background intensity
sources are greatly suppressed above 2 eV. We expect the main contributions tothis background intensity to follow a power-law model, including the tail of thezero-loss peak and vibrational losses (that are not resolved in this experiment).
From a spectrum image acquisition, we identify and sum the spectra in a
homogeneous area of the specimen. We carefully ﬁt a model to the resulting
spectrum that incorporates expressions for the power-law background and bandgap contributions. In our model, signals in the region of an energy gap Et are
represented by the following expression,sðEÞ ¼ ΘðE  Et ÞðE  Et Þr;
1 þ ekðEEt Þ

ð7Þ

where Θ is the Heaviside step function and r is a factor indicating the nature of thetransition, either 0.5 or 1.5 for direct or indirect transitions, respectively. In otherwords, in the former case, Et is the optical gap. These parameters stem from theexpected shape of the EELS signal close to the absorption onset according to thejoint density of states and matrix element for single-electron transitions between
parabolic bands67. The sigmoid function ﬁxed by the parameter k is used torepresent the decay of the signal far away from the absorption onset where theparabolic approximation does not hold anymore and the joint density of states
associated with the transition drops. We let the parameter k vary to tune the decay
far away from the main absorption onset in order to highlight the weak signal
coming from indirect transitions and ﬁx it to k = 0 for the direct transitions (nodecay). This heuristic is inspired by the behavior of the excitation signal dictated by
the Tauc-Lorentz model that is employed in the study of dielectric properties ofsemiconductor materials43. Poissonian noise variance of the EELS data is taken into
account for the model-based ﬁt49. This algorithm also calculates the standard
deviation for the obtained parameters68. The presented uncertainties correspond tothese values. In some cases, the standard deviation of the model parameters is well
below our estimate for the energy resolution. In these cases, we choose to report the
ZLP-FWHM value as the measurement uncertainty.
For most materials, the measurement of valence properties such as the band gap
using EELS requires considering the impact of various spurious sources, among
which relativistic losses are typically most problematic40. BaSnO3 is no exception,and for transmitted electrons at 60 kV accelerating voltage, the Cherenkov
threshold c2 =v2 ’ 5<Reε indicates that in this material relativistic losses might
contribute to EELS at the vicinity of the band gap and above, i.e., ~3–10 eV.
Experimental techniques that aim at reducing or suppressing the impact of bulk
relativistic losses (also known as Cherenkov-loss) have to be carefully tailored asthey depend on the material in a non-trivial manner.
Perhaps the most popular method consists of reducing the accelerating voltage
aiming to “slow down" the transmitted electrons below the Cherenkov
threshold41,69. This threshold is material-speciﬁc, and in many cases, it lies well
below the voltages that are attainable in most STEM instruments. An alternative
method is using off-axis acquisition geometries (sometimes also called dark-ﬁeld
EELS), eluding most of the relativistic losses since these appear at very small
scattering angles39,42. These techniques typically require careful experimental setup, and in most cases, convergent-beam electron diffraction needs to beconsidered, which is again sample-speciﬁc.
With the aim to address these issues, we also acquire spectra with larger energy
dispersion, up to around 100 eV, including all transitions from the valence bands,
some core transitions, and collective excitation of bulk and surface plasmons. In orderto study the bulk dielectric properties of BaSnO3, we remove plural scattering, using
Fourier-log deconvolution, and apply rKKA, using an in-house developed
algorithm43. For the latter, we normalize the experimental EELS using a reference
refractive index, nBaSnO3 = 2.05, achieving convergence after <10 iterations. We
monitor the convergence by computing the chi-square test between experimental andcorrected spectra, with a target value of X2 = 10−4. This results in an estimate of thecomplex dielectric function, ε(E), and of the sample-region thickness of around
120 nm, which is probably underestimated because of beam broadening.
Optical absorption measurements. Optical transmittance spectra are recorded
from 5 to 300 K using a Lambda 19 (PerkinElmer) spectrophotometer and a liquid
helium cryostat (Oxford Instruments). The used sample of 150 μm thickness isdouble side polished. Absorption coefﬁcients are calculated from the transmittance

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data by approximately taking account of the reﬂection losses setting the refraction
index to 2. More details can also be found in refs. 22,48.

Data availability
Input and output ﬁles can be downloaded free of charge from the NOMAD Repository70
at the following link: https://doi.org/10.17172/NOMAD/2021.05.10-1. The EELS andrKKA-EELS data can be found at https://doi.org/10.17172/NOMAD/2021.11.01-1. The
data of the case with optimized lattice parameter can be found at https://doi.org/
10.17172/NOMAD/2021.02.25-1.

Code availability
The code exciting is available at exciting-code.org.

Received: 25 June 2021; Accepted: 2 February 2022;

References
1.
2.
3.

4.
5.

6.

7.
8.

9.
10.

11.
12.
13.

14.

15.
16.

17.
18.

19.

20.
21.

22.

Kim, H. J. et al. High mobility in a stable transparent perovskite oxide. Appl.
Phys. Express 5, 061102 (2012).
Shin, S. S. et al. Improved quantum efﬁciency of highly efﬁcient perovskite
BaSnO3-based dye-sensitized solar cells. ACS Nano 7, 1027–1035 (2013).
Kim, H. J. et al. Physical properties of transparent perovskite oxides (Ba, La)
SnO3 with high electrical mobility at room temperature. Phys. Rev. B 86,
165205 (2012).
Kim, U. et al. All-perovskite transparent high mobility ﬁeld effect using
epitaxial BaSnO3 and LaInO3. APL Mater. 3, 036101 (2015).
Shin, J., Kim, Y. M., Kim, Y., Park, C. & Char, K. High mobility BaSnO3 ﬁlms
and ﬁeld effect transistors on non-perovskite MgO substrate. Appl. Phys. Lett.
109, 262102 (2016).
Zhu, L. et al. Performance enhancement of perovskite solar cells using a Ladoped BaSnO3 electron transport layer. J. Mater. Chem. A 5, 3675–3682(2017).
Niedermeier, C. A. et al. Electron effective mass and mobility limits indegenerate perovskite stannate BaSnO3. Phys. Rev. B 95, 161202 (2017).
Krishnaswamy, K., Himmetoglu, B., Kang, Y., Janotti, A. & Van de Walle, C.
G. First-principles analysis of electron transport in BaSnO3. Phys. Rev. B 95,
205202 (2017).
Lee, W.-J. et al. Transparent perovskite barium stannate with high electron
mobility and thermal stability. Annu. Rev. Mater. Res. 47, 391–423 (2017).
Paudel, T. R. & Tsymbal, E. Y. Prediction of a mobile two-dimensional
electron gas at the LaScO3/BaSnO3(001) interface. Phys. Rev. B 96, 245423(2017).
Krishnaswamy, K. et al. BaSnO3 as a channel material in perovskite oxide
heterostructures. Appl. Phys. Lett. 108, 083501 (2016).
Kim, Y. M. et al. Interface polarization model for a 2-dimensional electron gas
at the BaSnO3/LaInO3 interface. Sci. Rep. 9, 16202 (2019).
Zupancic, M. et al. Role of the interface in controlling the epitaxial
relationship between orthorhombic LaInO3 and cubic BaSnO3. Phys. Rev.
Mater. 4, 123605 (2020).
Aggoune, W. & Draxl, C. Tuning two-dimensional electron and hole gases at
LaInO3/BaSnO3 interfaces by polar distortions, termination, and thickness.
Npj Comput. Mater. 7, 174 (2021).
Mizoguchi, H., Woodward, P. M., Park, C.-H. & Keszler, D. A. Strong nearinfrared luminescence in BaSnO3. J. Am. Chem. Soc. 126, 9796–9800 (2004).
Hadjarab, B., Bouguelia, A. & Trari, M. Optical and transport properties oflanthanum-doped stannate BaSnO3. J. Phys. D Appl. Phys. 40, 5833–5839(2007).
Luo, X. et al. High carrier mobility in transparent Ba1−xLaxSnO3 crystals witha wide band gap. Appl. Phys. Lett. 100, 172112 (2012).
Stanislavchuk, T. N., Sirenko, A. A., Litvinchuk, A. P., Luo, X. & Cheong, S.W. Electronic band structure and optical phonons of BaSnO3 andBa0.97La0.03SnO3 single crystals: theory and experiment. J. Appl. Phys. 112,044108 (2012).
Kang, Y., Peelaers, H., Krishnaswamy, K. & Van de Walle, C. G. Firstprinciples study of direct and indirect optical absorption in BaSnO3. Appl.
Phys. Lett. 112, 062106 (2018).
Seo, D. et al. Infrared-optical spectroscopy of transparent conducting
perovskite (La, Ba)SnO3 thin ﬁlms. Appl. Phys. Lett. 104, 022102 (2014).
Chambers, S. A., Kaspar, T. C., Prakash, A., Haugstad, G. & Jalan, B. Bandalignment at epitaxial BaSnO3/SrTiO3(001) and BaSnO3/LaAlO3(001)heterojunctions. Appl. Phys. Lett. 108, 152104 (2016).
Galazka, Z. et al. Melt growth and properties of bulk BaSnO3 single crystals. J.
Phys. Condens. Matter 29, 075701 (2016).

ARTICLE

23. Yun, H. et al. Electronic structure of BaSnO3 investigated by high-energyresolution electron energy-loss spectroscopy and ab initio calculations. J. Vac.
Sci. Technol. A 36, 031503 (2018).
24. Terry, R. J., Combs, N., McMillen, C. D., Stemmer, S. & Kolis, J. W.
Hydrothermal growth of BaSnO3 single crystals for wide bandgap
applications. J. Cryst. Growth 536, 125529 (2020).
25. Dabaghmanesh, S., Saniz, R., Amini, M. N., Lamoen, D. & Partoens, B.
Perovskite transparent conducting oxides: an ab initio study. J. Phys. Condens.
Matter 25, 415503 (2013).
26. Scanlon, D. O. Defect engineering of BaSnO3 for high-performancetransparent conducting oxide applications. Phys. Rev. B 87, 161201 (2013).
27. Kim, B. G., Jo, J. & Cheong, S. Hybrid functional calculation of electronic andphonon structure of BaSnO3. J. Solid State Chem. 197, 134–138 (2013).
28. Monserrat, B., Dreyer, C. E. & Rabe, K. M. Phonon-assisted optical absorption
in BaSnO3 from ﬁrst principles. Phys. Rev. B 97, 104310 (2018).
29. Joo, B. S. et al. Evidence for indirect band gap in BaSnO3 using angle-resolved
photoemission spectroscopy. Curr. Appl. Phys. 17, 595–599 (2017).
30. James Allen, S., Raghavan, S., Schumann, T., Law, K.-M. & Stemmer, S.
Conduction band edge effective mass of La-doped BaSnO3. Appl. Phys. Lett.
108, 252107 (2016).
31. Moreira, E. et al. Structural and optoelectronic properties, and infrared
spectrum of cubic BaSnO3 from ﬁrst principles calculations. J. Appl. Phys. 112,043703 (2012).
32. Krukau, A. V., Vydrov, O. A., Izmaylov, A. F. & Scuseria, G. E. Inﬂuence ofthe exchange screening parameter on the performance of screened hybrid
functionals. J. Chem. Phys. 125, 224106 (2006).
33. Hedin, L. New method for calculating the one-particle green’s function
with application to the electron gas problem. Phys. Rev. 139, A796–A823(1965).
34. Hybertsen, M. S. & Louie, S. G. First-principles theory of quasiparticles:
calculation of band gaps in semiconductor and insulators. Phys. Rev. Lett. 55,
1418–1421 (1985).
35. Hanke, W. & Sham, L. J. Many-particle effects in the optical spectrum of asemiconductor. Phys. Rev. B 21, 4656–4673 (1980).
36. Strinati, G. Application of the green functions method to the study of the
optical properties of semiconductors. Riv. Nuovo Cimento 11, 1–86 (1988).
37. Puschnig, P. & Ambrosch-Draxl, C. Optical absorption spectra ofsemiconductors and insulators including electron-hole correlations: an abinitio study within the lapw method. Phys. Rev. B 66, 165105 (2002).
38. Egerton, R. F. Electron Energy-loss Spectroscopy in the Electron Microscope(Springer Science & Business Media, 2011).
39. Gu, L. et al. Band-gap measurements of direct and indirect semiconductors
using monochromated electrons. Phys. Rev. B 75, 195214 (2007).
40. Stöger-Pollach, M., Laister, A. & Schattschneider, P. Treating retardation
effects in valence eels spectra for kramers–kronig analysis. Ultramicroscopy
108, 439–444 (2008).
41. Kaiser, U. et al. Transmission electron microscopy at 20 kv for imaging andspectroscopy. Ultramicroscopy 111, 1239–1246 (2011).
42. Korneychuk, S., Guzzinati, G. & Verbeeck, J. Measurement of the indirect
band gap of diamond with eels in stem. Phys. Status Solidi A 215, 1800318(2018).
43. Eljarrat, A. & Koch, C. T. Design and application of a relativistic kramerskronig analysis algorithm. Ultramicroscopy 206, 112825 (2019).
44. Singh, D. J., Xu, Q. & Ong, K. P. Strain effects on the band gap and opticalproperties of perovskite srsno3 and basno3. Appl. Phys. Lett. 104, 011910(2014).
45. Soleimanpour, S. & Kanjouri, F. First principle study of electronic and opticalproperties of the cubic perovskite BaSnO3. Phys. B Condens. Matter 432,
16–20 (2014).
46. Schleife, A. & Bechstedt, F. Ab initio description of quasiparticle band
structures and optical near-edge absorption of transparent conducting oxides.
J. Mater. Res. 27, 2180–2189 (2012).
47. Gori, P. et al. Optical spectra of ZnO in the far ultraviolet: ﬁrst-principles
calculations and ellipsometric measurements. Phys. Rev. B 81, 125207 (2010).
48. Aggoune, W. et al. Fingerprints of optical absorption in the perovskite LaInO3:
insight from many-body theory and experiment. Phys. Rev. B 103, 115105(2021).
49. de la Peña, F. et al. hyperspy: Hyperspy 1.0.1. https://doi.org/10.5281/
zenodo.58841 (2016).
50. Gass, M. H., Papworth, A. J., Beanland, R., Bullough, T. J. & Chalker, P. R.
Mapping the effective mass of electrons in III - V semiconductor quantum
conﬁned structures. Phys. Rev. B 73, 035312 (2006).
51. O’Donnell, K. P. & Chen, X. Temperature dependence of semiconductor bandgaps. Appl. Phys. Lett. 58, 2924–2926 (1991).
52. Irmscher, K. et al. On the nature and temperature dependence of thefundamental band gap of In2O3. Phys. Status Solidi A 211, 54–58 (2014).
53. Kok, D. J. et al. Temperature-dependent optical absorption of SrTiO3. Phys.
Status Solidi A 212, 1880–1887 (2015).

COMMUNICATIONS MATERIALS | (2022)3:12 | https://doi.org/10.1038/s43246-022-00234-6 | www.nature.com/commsmat

9

ARTICLE

COMMUNICATIONS MATERIALS | https://doi.org/10.1038/s43246-022-00234-6

54. Morris, A. J. & Monserrat, B. Optical absorption driven by dynamical
symmetry breaking in indium oxide. Phys. Rev. B 98, 161203 (2018).
55. Olovsson, W. et al. Vibrational effects in x-ray absorption spectra of
two-dimensional layered materials. J. Phys. Chem. C 123, 9688–9692(2019).
56. Karsai, F., Humer, M., Flage-Larsen, E., Blaha, P. & Kresse, G. Effects ofelectron-phonon coupling on absorption spectrum: K edge of hexagonalboron nitride. Phys. Rev. B 98, 235205 (2018).
57. Hohenberg, P. & Kohn, W. Inhomogeneus electron gas. Phys. Rev. 136,
B864–B871 (1964).
58. Kohn, W. & Sham, L. J. Self-consistent equations including exchange andcorrelation effects. Phys. Rev. 140, A1133–A1138 (1965).
59. Perdew, J. P. et al. Restoring the density-gradient expansion for exchange insolids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).
60. Tillack, S., Gulans, A. & Draxl, C. Maximally localized wannier functions
within the (L)APW + LO method. Phys. Rev. B 101, 235102 (2020).
61. Gulans, A. et al. exciting: a full-potential all-electron package implementing
density-functional theory and many-body perturbation theory. J. Phys.
Condens. Matter 26, 363202 (2014).
62. Nabok, D., Gulans, A. & Draxl, C. Accurate all-electron G0W0 quasiparticle
energies employing the full-potential augmented planewave method. Phys.
Rev. B 94, 035118 (2016).
63. Vorwerk, C., Aurich, B., Cocchi, C. & Draxl, C. Bethe–Salpeter equation forabsorption and scattering spectroscopy: implementation in the exciting code.
Electron. Struct. 1, 037001 (2019).
64. Gillet, Y., Giantomassi, M. & Gonze, X. First-principles study of excitonic
effects in raman intensities. Phys. Rev. B 88, 094305 (2013).
65. Gao, J., Wu, Q., Persson, C. & Wang, Z. Irvsp: to obtain irreducible
representations of electronic states in the VASP. Comput. Phys. Commun. 261,
107760 (2021).
66. Momma, K. & Izumi, F. VESTA3 for three-dimensional visualization of
crystal, volumetric and morphology data. J. Appl. Cryst. 44, 1272–1276(2011).
67. Rafferty, B. & Brown, L. M. Direct and indirect transitions in the region of theband gap using electron-energy-loss spectroscopy. Phys. Rev. B 58,
10326–10337 (1998).
68. Zamani, R. R. et al. Unraveling electronic band structure of narrow-bandgap
p-n nanojunctions in heterostructured nanowires. Phys. Chem. Chem. Phys.
23, 25019–25023 (2021).
69. Cañas, J. et al. Determination of alumina bandgap and dielectric functions of
diamond mos by stem-veels. Appl. Surf. Sci. 461, 93–97 (2018).
70. Draxl, C. & Schefﬂer, M. The NOMAD laboratory: from data sharing to
artiﬁcial intelligence. J. Phys. Mater. 2, 036001 (2019).

Acknowledgements
This work was supported by the project BaStet (Leibniz Senatsausschuss Wettbewerb,
No. K74/2017) that is embedded in the framework of GraFOx, a Leibniz ScienceCampus,
partially funded by the Leibniz Association. We acknowledge the North-German
Supercomputing Alliance (HLRN, project bep00078) for providing HPC resources. A.E.,

10

C.K., and C.D. appreciate partial funding by the Deutsche Forschungsgemeinschaft(DFG) - Projektnummer 182087777 - SFB951. W.A. thanks Cecilia Vona for implementing the HSE functional in the exciting code and Le Fang and Christian Vorwerk
for fruitful discussions. We acknowledge support by the Open Access Publication Fundof Humboldt-Universität zu Berlin.

Author contributions
W.A. performed the ab initio calculations and analyzed the data. A.E. and K.I. measured
and analyzed the EELS and optical absorption data, respectively; Z.G. grew the single
crystals; M.Z. prepared the samples. W.A., A.E., D.N., K.I., M.Z., Z.G., M.A., C.K., andC.D. discussed the results.

Funding
Open Access funding enabled and organized by Projekt DEAL.

Competing interests
The authors declare no competing interests.

Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s43246-022-00234-6.
Correspondence and requests for materials should be addressed to Wahib Aggoune.
Peer review information Communications Materials thanks the anonymous reviewers
for their contribution to the peer review of this work. Primary handling editor: Aldo
Isidori.
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