Supporting information for:
Cobalt (II) oxide and nickel (II) oxide
alloys as potential intermediate-band
semiconductors: A theoretical study
Nima Alidoust,1 Martina Lessio 2 and Emily A. Carter3,*
Departments of 1Electrical Engineering, 2Chemistry and 3Mechanical and Aerospace
Engineering, Program in Applied and Computational Mathematics, and Andlinger Center for
Energy and the Environment, Princeton University, Princeton, NJ 08544-5263
S1 - Absorption spectrum for Co0.25Ni0.75O as calculated by –Im(𝝐)
Figure S1 – Negative of the imaginary part of the dielectric function −Im (𝜖) resulting from
G0W0 calculations for Co0.25Ni0.75O.
*
Corresponding author: eac@princeton.edu
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Fig. S1 shows the negative of the imaginary part of the dielectric function −Im (𝜖) for
Co0.25Ni0.75O and is comparable to Fig. 6 in the Main Text, which depicts the corresponding
function for pure NiO and CoO. The broad peak at 𝐸 = 3.3 eV indicates that strong optical
absorption occurs between the VBE and CBE of Co0.25Ni0.75O, the atomic orbital characters of
which are demonstrated in Fig. 8 (b) of the Main Text. Furthermore, Fig. S1 clearly shows that
alloying NiO and CoO does not deleteriously affect the optical properties of CoO when it comes
to light absorption, given that the lowest peak in −Im (𝜖) for CoO occurs at 𝐸 = 3.9 eV.
However, despite the double-gap structure clearly observed in the electronic structure of
Co0.25Ni0.75 (Fig. 8 (b)), −Im (𝜖) for this alloy does not have a double-peak or shoulder structure,
similar to what is observed in Fig. 6 for pure CoO. The likely reason for this is the fact that
intermediate band in Co0.25Ni0.75O is considerably wider than that of pure CoO (Fig. 5). This
means that, compared to the case for CoO, any peak associated with electronic transitions to the
intermediate band in Co0.25Ni0.75 are likely to be much stronger and wider than the peaks
associated with electronic transitions to the upper band (i.e., the band that extends from 4.1-4.8
eV in Fig. 8 (b)). Therefore, it is very likely that the peak associated with electronic transitions to
the upper band would merge into the peak associated with transitions to the intermediate band.
Therefore the former is unlikely to be visible in the −Im (𝜖) plot in Fig. 6 and no double-peak
or shoulder structure is observed.
Given this limitation of the absorption spectrum in this
specific case, other tests should be performed to validate the double-gap structure of
Co0.25Ni0.75O. Possible measurements for this purpose are absorption spectroscopy and resonant
inelastic X-ray scattering1,2 (more suitable for studying d-d transitions), in the presence of solar
concentrators, which would allow for significant partial occupation of the intermediate band and
2
therefore would enable transitions from this band to the upper band. If transitions to the upper
band indeed occur, a distinct peak must appear at energies well below the peak at 3.3 eV.
S2 - Assessment of potential polaronic character of electrons in the Co0.25Ni0.75 conduction
band
Elucidating the transport mechanism for electrons in the conduction band of Co0.25Ni0.75
is crucial in determining the ultimate viability of this alloy in solar energy applications. To
evaluate whether transport in Co0.25Ni0.75 conduction band is polaronic (i.e., occurs by transfer of
localized carriers between individual sites), we used DFT+U theory with the LDA exchangecorrelation functional and U – J = 3.8 eV and 4.0 eV for Ni and Co ions, respectively, to assess
whether an added electron would be localized on any individual site. We introduced an extra
electron to the unit cell depicted in Fig. 3 (c) of the main text together with a positive uniform
compensating background charge. The compensating charge prevents the divergence of
Coulomb potential due to the periodic boundary conditions when an extra electron is added to
the system. We employed the same computational parameters (k-point mesh, kinetic energy
cutoff for the planewave basis, and number of bands) that we used for studying the DFT+U
ground state of the case without an added electron (cf. Computational Methods, section “NiOCoO alloys”).
We attempted to localize the electron on a Co or Ni site by reducing the magnetization of
these high-spin ions in the initial guess for the wavefunction, as well by locally distorting the
lattice (expanding all the metal-oxygen bonds by 0.3 Å around the cation with reduced
magnetization) in the initial guess for the structure. Such an initial guess sets up the best possible
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scenario to find a small polaron state. For Co, reducing the magnetization is equivalent to adding
a spin-down electron to the 3d (t2g) orbitals depicted in Fig. 2, the high-spin case in the main text.
For Ni ions, reducing the magnetization is equivalent to adding an electron to the singly occupied
3d (eg) orbitals. We then relaxed the structure to find the equilibrium geometry distorted by the
added electron. The DFT+U ground state resulting from our calculations neither contains a local
distortion of the lattice nor a localized electron; the electron rather is delocalized over the entire
cell. This can be seen from the changes in Bader charges for individual ions in Table S1. Bader
charge analysis gives the charge in the vicinity of each atom by integrating electronic charge in
an area confined by zero-flux surfaces in the overall charge density.2,3,4 Before adding the extra
electron the charge on Ni and Co ions ranges from ~ +1.08 e to +1.19 e. The charge on the O
ions is ~ -1.11 e to -1.14 e. Note that this charge deviates from the formal charge 2e, indicating
considerable covalent character in the metal-oxygen bonds. Adding an electron to the system
leads to a reduction of charge in all of the cations. The charge on Ni and Co ions in the case with
an added electron has a reduced range from 0.98 e to 1.04 e, while the range for the charge on O
becomes more negative, -1.12 e to -1.18 e. Overall, of the -1e charge added to the unit cell, -0.35
e is distributed on Ni ions, -0.42 e on Co ions, and -0.24 e on O ions. This clearly shows that the
electron does not unambiguously belong to a single site and therefore, it does not form a polaron.
This means that electrons in the conduction band of Co0.25Ni0.75 are likely to be free electrons,
hence having superior transport properties to those of many other transition-metal oxides with a
dominant polaronic electron transport. This is further evidence of the potential of Co0.25Ni0.75 as a
parent-IBSC material for use in solar energy conversion applications.
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Table S1 – Bader charge analysis on the individual ions before and after adding an extra electron
to the Co0.25Ni0.75 unit cell (Figure 3 (c) of the main text).
Ion
Ni
Ni
Ni
Ni
Ni
Ni
O
O
O
O
O
O
O
O
Co
Co
Bader charge before
adding an electron
(e)
1.09
1.09
1.09
1.09
1.08
1.09
-1.11
-1.12
-1.14
-1.1
-1.11
-1.11
-1.12
-1.1
1.19
1.19
Bader charge
after adding an
electron
(e)
1.03
1.02
1.04
1.03
1.04
1.02
-1.16
-1.14
-1.18
-1.12
-1.13
-1.13
-1.16
-1.13
0.98
0.98
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Difference in Bader
charge upon adding an
electron
(e)
-0.06
-0.07
-0.05
-0.06
-0.04
-0.07
-0.05
-0.02
-0.04
-0.02
-0.02
-0.02
-0.04
-0.03
-0.21
-0.21
References
(1) L. Andrew Wray, J. Li, Z. Q. Qiu, Jinsheng Wen, Zhijun Xu, Genda Gu, Shih-Wen Huang,
Elke Arenholz, Wanli Yang, Zahid Hussain, and Yi-De Chuang Rev. Mod. Phys., 2011, 83, No.
2, 706-763
(2) W. Tang, E. Sanville, and G. Henkelman, J. Phys.: Condens. Matter 21, 084204 (2009).
(3) E. Sanville, S. D. Kenny, R. Smith, and G. Henkelman J. Comp. Chem. 28, 899-908 (2007).
(4) G. Henkelman, A. Arnaldsson, and H. Jónsson, Comput. Mater. Sci. 36, 254-360 (2006).
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