Supplementary Materials
Supplementary Materials to accompany
Effective Masses and Electronic and Optical Properties of Nontoxic MASnX3 (X=Cl, Br, and I) Perovskite Structures as Solar Cell Absorber: A Theoretical Study Using HSE06
by
Jing Feng1 and Bing Xiao2*
1. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA 2. Department of Physics, College of Science and Engineering, Temple University, Philadelphia, PA, 19122, USA.
Supporting Information Placeholder
(Dated: August 3, 2014)
1
1 Details and methods The first principles calculations1 were conducted using the plane wave basis in CASTEP code 2
, similar to the previous ref 3. The norm-conserving type pesudopotentials (NCPPs)4 within the
frozen core approximation were employed in this work, i.e., H1s, C2s2p, N2s2p, I5s5p, Br4s4p and Sn5s5p. The Monkhorst-Pack type k-mesh used in our calculations was 10 × 8 × 10. The kinetic energy cutoff was set to 900 eV. In our calculations, the dispersion interactions were computed from an empirical pair-wise corrections proposed by Grimme 5 in terms of DFT+D2 scheme. The exchange-correlation functional of DFT part was computed by Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA)6. In order to have a better description for the fundamental band gap from DFT, we employed the range-separated hybrid functional by means of HSE06 to calculate the band structures and optical spectra of CH3NH3SnX3 (Cl, Br and I) phases7.
2 Lattice parameters of CH3NH3SnX3 (X= Cl, Br and I) compounds Table S1 Calculated equilibrium lattice parameters of CH3NH3SnX3 (X=Cl, Br, I) perovskites. Structure
CH3NH3SnCl3
a
b
c
V
(Å)
(Å)
(Å)
(Å3)
7.905 11.067 7.550 660.5
CH3NH3SnBr3 8.144 11.546 7.813 734.7 CH3NH3SnI3
8.556 12.428 8.326 885.4
2
Table S2 Fractional atomic coordinates of Sn, X, N, C and H elements in orthorhombic-MASnXI3 (X=Cl, Br, I) structure (Space group Pnma (No. 62)). CH3NH3SnCl3 x
y
z
Occupation
Wyckoff Site
Sym.
1
Cl
I1
0.20357
0.00402
0.20056
1
8d
1
2
H
H2
0.38779
0.33179
0.37391
1
8d
1
3
H
H3
0.60110
0.32554
0.60478
1
8d
1
4
Sn
Pb4
0.50000
0.00000
0.00000
1
4b
-1
5
Cl
I5
0.47333
0.25000
-0.05850
1
4c
.m.
6
C
C6
0.90406
0.25000
0.04668
1
4c
.m.
7
H
H7
0.31543
0.25000
0.56401
1
4c
.m.
8
H
H8
0.67072
0.25000
0.42920
1
4c
.m.
9
N
N9
0.92024
0.75000
0.02722
1
4c
.m.
CH3NH3SnBr3 x
y
z
occupation
Wyckoff Site
Sym.
1
Br
I1
0.19460
0.00802
0.19057
1
8d
1
2
H
H2
0.38859
0.32844
0.37763
1
8d
1
3
H
H3
0.59855
0.32243
0.59768
1
8d
1
4
Sn
Pb4
0.50000
0.00000
0.00000
1
4b
-1
5
Br
I5
0.47252
0.25000
-0.06668
1
4c
.m.
6
C
C6
0.90523
0.25000
0.04571
1
4c
.m.
7
H
H7
0.32109
0.25000
0.56303
1
4c
.m.
8
H
H8
0.66342
0.25000
0.42653
1
4c
.m.
9
N
N9
0.92314
0.75000
0.02310
1
4c
.m.
CH3NH3SnI3 x
y
z
Occupation
Wyckoff Site
Sym.
1
I
I1
0.18837
0.01221
0.18414
1
8d
1
2
H
H2
0.39240
0.32276
0.38346
1
8d
1
3
H
H3
0.59402
0.31701
0.58944
1
8d
1
4
Sn
Pb4
0.50000
0.00000
0.00000
1
4b
-1
5
I
I5
0.47588
0.25000
-0.07190
1
4c
.m.
3
6
C
C6
0.90895
0.25000
0.04414
1
4c
.m.
7
H
H7
0.32984
0.25000
0.55904
1
4c
.m.
8
H
H8
0.65574
0.25000
0.42816
1
4c
.m.
9
N
N9
0.92678
0.75000
0.01900
1
4c
.m.
4
3 Electronic structures of CH3NH3SnX3 (X= Cl, Br and I) compounds The electronic structures of CH3NH3SnX3 (X= Cl, Br and I) compounds were calculated using HSE06 5 in this work. Note that all calculations for hybrid functional were carried out on the top of PBE+D2 structures. The obtained band dispersions of CH3NH3SnX3 (X= Cl, Br and I) compounds are illustrated in Figure s1. One should note that in the framework of DFT, the fundamental band gap is not a ground state property of condensed phase; therefore, even within the exact exchange-correlation functional, the Kohn-Sham single particle band gap is still not exactly the same as the physical band gap, missing the derivative continuity in the exchangecorrelation functional at the integer number of electrons. CH3NH3SnCl3
CH3NH3SnBr3
8
8
6
6 Violet 3.2 eV
2
gap=2.8 eV Red 1.6 eV
0
Violet 3.2 eV
4
Energy ( eV )
Energy ( eV )
4
2
gap=2.0 eV
-2
-2
-4
-4
-6
Red 1.6 eV
0
-6
R
U
Y
Z
X
S
T
R
Γ
U
Y
Z
X
S
T
Γ
CH3NH3SnI3 8 6 Violet 3.2 eV
Energy ( eV )
4 2
gap=1.7 eV
Red 1.6 eV
0 -2 -4 -6
R
U
Y
Z
X
S
T
Γ
Figure S1 Calculated band structure of CH3NH3SnX3 (X=Cl, Br, I) perovskites. The dispersion curves are shown along the directions R→U→Y→Z→X→S→T→Γ, where R = (-1/2, 1/2, 1/2), U = (0, 1/2, 1/2), Y = (0, 1/2, 0), Z = (0, 0, 1/2), X = (1/2, 0, 0), S = (1/2, 0, 1/2), T = (0, 0, 1/2) and Γ= (0, 0, 0). The dashed line is the Fermi level.
5
CH3NH3SnCl3
-1
.
-1
.
30
20
10
0
30
20
10
0 -25
-20
-15
-10
-5
0
5
10
-25
Energy ( eV )
-20
-15
-10
-5
Energy ( eV )
CH3NH3SnI3
MA I Sn
40
.
-1
Density of states ( states cell )
MA Br Sn
40
Density of states ( states cell )
40
Density of states ( states cell )
CH3NH3SnBr3
MA Cl Sn
30
20
10
0 -25
-20
-15
-10
-5
0
5
10
Energy ( eV )
Figure S2 Calculated density of states of CH3NH3SnX3 (X=Cl, Br, I) perovskites.
6
0
5
10
4 The changes of band gap and Fermi energy of CH3NH3SnX3 (X= Cl, Br and I) compounds as a function of isotropic stress (a)
(b)
Compression
Tension
2.8
0.5
Compression
0.0
Fermi energy ( eV )
Energy gap ( eV )
2.6
Tension
2.4 2.2 2.0 1.8
-0.5
-1.0
CH3NH3SnCl3 1.6 1.4 -2.0
CH3NH3SnCl3
CH3NH3SnBr3
CH3NH3SnBr3
-1.5
CH3NH3SnI3 -1.5
-1.0
CH3NH3SnI3 -0.5
0.0
0.5
1.0
1.5
2.0
-2.0
Stress ( GPa )
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Stress ( GPa )
Figure S3 Effects of isotropic stress on fundamental band gap (a) and Fermi level (b) of CH3NH3SnX3 (X=Cl, Br, I) perovskites. Fermi energy referrers to the top of valence band.
7
5 The dielectric function of CH3NH3SnX3 (X= Cl, Br and I) compounds under small hydrostatic stress -2 GPa Re -2 GPa Im -1GPa Re -1GPa Im -0.5 GPa Re -0.5 GPa Im 0 GPa Re 0 GPa Im
14
Dielectric Function
12 10
0.5 GPa Re 0.5 GPa Im 1 GPa Re 1 GPa Im 2 GPa Re 2 GPa Im
CH3NH3SnCl3
(a)
8 6 4 2 0 0
400
800
1200
1600
Wavelength ( nm )
-2 GPa Re -2 GPa Im -1 GPa Re -1 GPa Im -0.5 GPa Re -0.5 GPa Im 0 GPa Re 0 GPa Im
14
Dielectric Function
12 10
0.5 GPa Re 0.5 GPa Im 1 GPa Re 1 GPa Im 2 GPa Re 2 GPa Im
CH3NH3SnBr3 ( b )
8 6 4 2 0 0
400
800
1200
1600
Wavelength ( nm )
12
Dielectric Function
CH3NH3SnI3
-2 GPa Re -2 GPa Im -1 GPa Re -1GPa Im -0.5 GPa Re -0.5 GPa Im 0 GPa Re 0 GPa Im
14
10
(c)
8 0.5 GPa Re 0.5 GPa Im 1 GPa Re 1 GPa Im 2 GPa Re 2 GPa Im
6 4 2 0 0
400
800
1200
1600
Wavelength ( nm )
Figure S4 Calculated real and imaginary parts of dielectric spectra of CH3NH3SnX3 (X=Cl, Br, I) perovskites at different isotropic stresses. In (a) and (b), the dielectric spectra of CH3NH3SnBr3 calculated at 2 GPa are very different to those of under other pressures, indicating the effects of the decreasing of band gap and the change of effective mass on the optical properties. 8
References: 1. Hohenberg, P.; Kohn, W., Inhomogeneous Electron Gas. Phys Rev 1964, 136, B864. 2. Segall, M.; Lindan, P.; Probert, M.; Pickard, C.; Hasnip, P.; Clark, S.; Payne, M., First-principles simulation: ideas, illustrations and the CASTEP code. J Phys Condens Matter 2002, 14, 2717. 3. Feng, J.; Xiao, B., Correction to “Crystal Structures, Optical Properties, and Effective Mass Tensors of CH3NH3PbX3 (X = I and Br) Phases Predicted from HSE06”. The Journal of Physical Chemistry Letters 2014, 5, 1719-1720. 4. Hamann, D. R., Generalized norm-conserving pseudopotentials. Physical Review B 1989, 40, (5), 2980-2987. 5. Grimme, S., Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of Computational Chemistry 2006, 27, (15), 1787-1799. 6. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77, (18), 3865-3868. 7. Heyd, J., Scuseria, G.E., Ernzerhof, M., Hybrid functionals based on a screened Coulomb potential, The Journal of Chemical Physics, 2003, 118, 8207-8215.
9
Effective Masses and Electronic and Optical Properties of Nontoxic MASnX3 (X=Cl, Br, and I) Perovskite Structures as Solar Cell Absorber: A Theoretical Study Using HSE06
by
Jing Feng1 and Bing Xiao2*
1. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA 2. Department of Physics, College of Science and Engineering, Temple University, Philadelphia, PA, 19122, USA.
Supporting Information Placeholder
(Dated: August 3, 2014)
1
1 Details and methods The first principles calculations1 were conducted using the plane wave basis in CASTEP code 2
, similar to the previous ref 3. The norm-conserving type pesudopotentials (NCPPs)4 within the
frozen core approximation were employed in this work, i.e., H1s, C2s2p, N2s2p, I5s5p, Br4s4p and Sn5s5p. The Monkhorst-Pack type k-mesh used in our calculations was 10 × 8 × 10. The kinetic energy cutoff was set to 900 eV. In our calculations, the dispersion interactions were computed from an empirical pair-wise corrections proposed by Grimme 5 in terms of DFT+D2 scheme. The exchange-correlation functional of DFT part was computed by Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA)6. In order to have a better description for the fundamental band gap from DFT, we employed the range-separated hybrid functional by means of HSE06 to calculate the band structures and optical spectra of CH3NH3SnX3 (Cl, Br and I) phases7.
2 Lattice parameters of CH3NH3SnX3 (X= Cl, Br and I) compounds Table S1 Calculated equilibrium lattice parameters of CH3NH3SnX3 (X=Cl, Br, I) perovskites. Structure
CH3NH3SnCl3
a
b
c
V
(Å)
(Å)
(Å)
(Å3)
7.905 11.067 7.550 660.5
CH3NH3SnBr3 8.144 11.546 7.813 734.7 CH3NH3SnI3
8.556 12.428 8.326 885.4
2
Table S2 Fractional atomic coordinates of Sn, X, N, C and H elements in orthorhombic-MASnXI3 (X=Cl, Br, I) structure (Space group Pnma (No. 62)). CH3NH3SnCl3 x
y
z
Occupation
Wyckoff Site
Sym.
1
Cl
I1
0.20357
0.00402
0.20056
1
8d
1
2
H
H2
0.38779
0.33179
0.37391
1
8d
1
3
H
H3
0.60110
0.32554
0.60478
1
8d
1
4
Sn
Pb4
0.50000
0.00000
0.00000
1
4b
-1
5
Cl
I5
0.47333
0.25000
-0.05850
1
4c
.m.
6
C
C6
0.90406
0.25000
0.04668
1
4c
.m.
7
H
H7
0.31543
0.25000
0.56401
1
4c
.m.
8
H
H8
0.67072
0.25000
0.42920
1
4c
.m.
9
N
N9
0.92024
0.75000
0.02722
1
4c
.m.
CH3NH3SnBr3 x
y
z
occupation
Wyckoff Site
Sym.
1
Br
I1
0.19460
0.00802
0.19057
1
8d
1
2
H
H2
0.38859
0.32844
0.37763
1
8d
1
3
H
H3
0.59855
0.32243
0.59768
1
8d
1
4
Sn
Pb4
0.50000
0.00000
0.00000
1
4b
-1
5
Br
I5
0.47252
0.25000
-0.06668
1
4c
.m.
6
C
C6
0.90523
0.25000
0.04571
1
4c
.m.
7
H
H7
0.32109
0.25000
0.56303
1
4c
.m.
8
H
H8
0.66342
0.25000
0.42653
1
4c
.m.
9
N
N9
0.92314
0.75000
0.02310
1
4c
.m.
CH3NH3SnI3 x
y
z
Occupation
Wyckoff Site
Sym.
1
I
I1
0.18837
0.01221
0.18414
1
8d
1
2
H
H2
0.39240
0.32276
0.38346
1
8d
1
3
H
H3
0.59402
0.31701
0.58944
1
8d
1
4
Sn
Pb4
0.50000
0.00000
0.00000
1
4b
-1
5
I
I5
0.47588
0.25000
-0.07190
1
4c
.m.
3
6
C
C6
0.90895
0.25000
0.04414
1
4c
.m.
7
H
H7
0.32984
0.25000
0.55904
1
4c
.m.
8
H
H8
0.65574
0.25000
0.42816
1
4c
.m.
9
N
N9
0.92678
0.75000
0.01900
1
4c
.m.
4
3 Electronic structures of CH3NH3SnX3 (X= Cl, Br and I) compounds The electronic structures of CH3NH3SnX3 (X= Cl, Br and I) compounds were calculated using HSE06 5 in this work. Note that all calculations for hybrid functional were carried out on the top of PBE+D2 structures. The obtained band dispersions of CH3NH3SnX3 (X= Cl, Br and I) compounds are illustrated in Figure s1. One should note that in the framework of DFT, the fundamental band gap is not a ground state property of condensed phase; therefore, even within the exact exchange-correlation functional, the Kohn-Sham single particle band gap is still not exactly the same as the physical band gap, missing the derivative continuity in the exchangecorrelation functional at the integer number of electrons. CH3NH3SnCl3
CH3NH3SnBr3
8
8
6
6 Violet 3.2 eV
2
gap=2.8 eV Red 1.6 eV
0
Violet 3.2 eV
4
Energy ( eV )
Energy ( eV )
4
2
gap=2.0 eV
-2
-2
-4
-4
-6
Red 1.6 eV
0
-6
R
U
Y
Z
X
S
T
R
Γ
U
Y
Z
X
S
T
Γ
CH3NH3SnI3 8 6 Violet 3.2 eV
Energy ( eV )
4 2
gap=1.7 eV
Red 1.6 eV
0 -2 -4 -6
R
U
Y
Z
X
S
T
Γ
Figure S1 Calculated band structure of CH3NH3SnX3 (X=Cl, Br, I) perovskites. The dispersion curves are shown along the directions R→U→Y→Z→X→S→T→Γ, where R = (-1/2, 1/2, 1/2), U = (0, 1/2, 1/2), Y = (0, 1/2, 0), Z = (0, 0, 1/2), X = (1/2, 0, 0), S = (1/2, 0, 1/2), T = (0, 0, 1/2) and Γ= (0, 0, 0). The dashed line is the Fermi level.
5
CH3NH3SnCl3
-1
.
-1
.
30
20
10
0
30
20
10
0 -25
-20
-15
-10
-5
0
5
10
-25
Energy ( eV )
-20
-15
-10
-5
Energy ( eV )
CH3NH3SnI3
MA I Sn
40
.
-1
Density of states ( states cell )
MA Br Sn
40
Density of states ( states cell )
40
Density of states ( states cell )
CH3NH3SnBr3
MA Cl Sn
30
20
10
0 -25
-20
-15
-10
-5
0
5
10
Energy ( eV )
Figure S2 Calculated density of states of CH3NH3SnX3 (X=Cl, Br, I) perovskites.
6
0
5
10
4 The changes of band gap and Fermi energy of CH3NH3SnX3 (X= Cl, Br and I) compounds as a function of isotropic stress (a)
(b)
Compression
Tension
2.8
0.5
Compression
0.0
Fermi energy ( eV )
Energy gap ( eV )
2.6
Tension
2.4 2.2 2.0 1.8
-0.5
-1.0
CH3NH3SnCl3 1.6 1.4 -2.0
CH3NH3SnCl3
CH3NH3SnBr3
CH3NH3SnBr3
-1.5
CH3NH3SnI3 -1.5
-1.0
CH3NH3SnI3 -0.5
0.0
0.5
1.0
1.5
2.0
-2.0
Stress ( GPa )
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Stress ( GPa )
Figure S3 Effects of isotropic stress on fundamental band gap (a) and Fermi level (b) of CH3NH3SnX3 (X=Cl, Br, I) perovskites. Fermi energy referrers to the top of valence band.
7
5 The dielectric function of CH3NH3SnX3 (X= Cl, Br and I) compounds under small hydrostatic stress -2 GPa Re -2 GPa Im -1GPa Re -1GPa Im -0.5 GPa Re -0.5 GPa Im 0 GPa Re 0 GPa Im
14
Dielectric Function
12 10
0.5 GPa Re 0.5 GPa Im 1 GPa Re 1 GPa Im 2 GPa Re 2 GPa Im
CH3NH3SnCl3
(a)
8 6 4 2 0 0
400
800
1200
1600
Wavelength ( nm )
-2 GPa Re -2 GPa Im -1 GPa Re -1 GPa Im -0.5 GPa Re -0.5 GPa Im 0 GPa Re 0 GPa Im
14
Dielectric Function
12 10
0.5 GPa Re 0.5 GPa Im 1 GPa Re 1 GPa Im 2 GPa Re 2 GPa Im
CH3NH3SnBr3 ( b )
8 6 4 2 0 0
400
800
1200
1600
Wavelength ( nm )
12
Dielectric Function
CH3NH3SnI3
-2 GPa Re -2 GPa Im -1 GPa Re -1GPa Im -0.5 GPa Re -0.5 GPa Im 0 GPa Re 0 GPa Im
14
10
(c)
8 0.5 GPa Re 0.5 GPa Im 1 GPa Re 1 GPa Im 2 GPa Re 2 GPa Im
6 4 2 0 0
400
800
1200
1600
Wavelength ( nm )
Figure S4 Calculated real and imaginary parts of dielectric spectra of CH3NH3SnX3 (X=Cl, Br, I) perovskites at different isotropic stresses. In (a) and (b), the dielectric spectra of CH3NH3SnBr3 calculated at 2 GPa are very different to those of under other pressures, indicating the effects of the decreasing of band gap and the change of effective mass on the optical properties. 8
References: 1. Hohenberg, P.; Kohn, W., Inhomogeneous Electron Gas. Phys Rev 1964, 136, B864. 2. Segall, M.; Lindan, P.; Probert, M.; Pickard, C.; Hasnip, P.; Clark, S.; Payne, M., First-principles simulation: ideas, illustrations and the CASTEP code. J Phys Condens Matter 2002, 14, 2717. 3. Feng, J.; Xiao, B., Correction to “Crystal Structures, Optical Properties, and Effective Mass Tensors of CH3NH3PbX3 (X = I and Br) Phases Predicted from HSE06”. The Journal of Physical Chemistry Letters 2014, 5, 1719-1720. 4. Hamann, D. R., Generalized norm-conserving pseudopotentials. Physical Review B 1989, 40, (5), 2980-2987. 5. Grimme, S., Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of Computational Chemistry 2006, 27, (15), 1787-1799. 6. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77, (18), 3865-3868. 7. Heyd, J., Scuseria, G.E., Ernzerhof, M., Hybrid functionals based on a screened Coulomb potential, The Journal of Chemical Physics, 2003, 118, 8207-8215.
9
