CASTELLI, PANDEY, THYGESEN, AND JACOBSEN PHYSICAL REVIEW B 91, 165309 (2015)
FIG. 1. (Color online) Unit cell of the αβ structure. The cubic
perovskite planes are stacked in the z direction, while the x and y
directions maintain the usual periodicity of a cubic perovskite. α
indicates the BaSnO3 perovskite, and β the BaTaO2N.
properties of the materials due only to the different stackings,
regardless of any changes caused by structure relaxation.
Using GLLB-SC, BaSnO3 shows an indirect band gap
between the and R points of 3.33 eV, while BaTaO2N
is found to have a direct band gap at of 1.84 eV. This
compares favorably with experiments where the optical gaps
have been measured, through diffuse reflectance spectra, to 3.1
and 1.9 eV for BaSnO3 23 and BaTaO2N 24, respectively.
HSE calculations slightly underestimate the gaps (2.89 eV for
BaSnO3 and 1.71 eV for BaTaO2N).
Figure 2 reports the band gaps for the 36 αnαβnβ structures
as a function of the number of α and β planes. The gaps vary
considerably spanning a region of 1 eV, illustrating the high
degree of tunability of the band gap. The simplest combination
with only one layer of α and β in the heterostructure gives the
widest gap with a value of 2.26 eV, not too far from the average
of the band gaps of the two constituent cubic perovskites. (For
comparison, theHSE method gives again a slightly lower value
of 2.04 eV.) More complex combinations exhibit reduced band
FIG. 2. (Color online) Calculated band gaps as a function of the
number of α (BaSnO3) and β (BaTaO2N) layers. Each rectangle in
the plot represents a layered periodic structure with sequence αnβm.
FIG. 3. (Color online) Sketch of the electronic level positions at
an interface between layers of BaSnO3 and BaTaO2N. When the layer
thickness is reduced, the local position of the conduction-band edge
moves up due to confinement.
gaps depending on their composition. As we shall show in the
following, the significant complicated variation of the band
gap shown in Fig. 2 can essentially be understood in terms of
electronic confinement and tunneling effects.
In Fig. 3, we sketch how the local band edges are positioned
relative to each other for different layer thicknesses. For the
thickest layer structure, α6β6, we have the smallest band gap
of 1.26 eV. The state at the valence-band maximum (VBM)
is composed mainly of N2p orbitals with a minor contribution
from theO2p orbitals and is located in the β part of the material.
In fact, all of the mixed compositions have a direct band gap
at the point, with the VBM state of this character located
in the β part of the material. The character of the VBM state
can, for example, be seen in Figs. 4(a) and 4(c) for the αβ
and α2β structures, respectively. Not only is the character of
the VBM state the same for all structures, but the calculations
also indicate that it does not move much relative to a low-lying
atomic state in BaTaO2N, and we shall therefore regard this
level as fixed in the following and ascribe the variations to
changes in the conduction band.
FIG. 4. (Color online) Wave functions of states at the valenceband
maximum (VBM) and the conduction-band minimum (CBM)
for some combinations of α and β layers.