Supporting
material
for
manuscript:
“GeSe
monolayer
semiconductor with tunable direct band gap and small carrier
effective mass” by authors: Yonghong Hu, Shengli Zhang,
Shaofa Sun, Meiqiu Xie, Bo Cai, Haibo Zenga)
We optimize the structure of bulk GeSe and calculate the lattice parameters and energy band
gap through several different potential functions under GGA method (see table S1). It’s found that
the lattice parameters calculated by PW91 (a = 4.41 Å, b= 3.84 Å, and c= 10.82 Å) is more in
agreement with the previous theoretical and experimental results. So we mainly take this potential
function to calculate the structural properties of the bulk GeSe and GeSe monolayer. We also use
the HSE06 functions to calculate the energy band structure of bulk GeSe and GeSe monolayer. We
obtain an indirect band gap (1.29eV) of bulk GeSe (see table S2), which is close to the indirect
band gap (1.24) reported in reference [5] below. The calculated results of lattice parameters and
energy band gap of bulk GeSe (see table S1) are both in agreement with previous theoretical and
experimental results.
Computational details
+ These Authors contribute equally to this work. a) Authors to whom correspondence should be
addressed. Electronic addresses: zeng.haibo@njust.edu.cn
All of our calculations, including geometry relaxation and electronic structure calculation are
performed within the density functional theory (DFT) implemented in the CASTEP package with
an ultrasoft pseudo-potential. 1 The exchange–correlation functional is treated using a generalized
gradient approximation (GGA). 2 Various potential functions under GGA method, such as PW91,
PBE and PBESOL etc., are tested and compared, and the potential function of PW91 is found to
be the most suited for our system (see the supporting materials and table S1-S3). A sufficiently
large 20 Å vacuum region is used to separate the two-dimensional structures to rule out any
interaction among the neighboring layers along c-axis. The basis set of valence electronic states is
set to be 4s24p2 for Ge and 4s24p4 for Se. The structure is optimized with the
Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.3 In calculations, the electronic wave
functions are expanded in a plane-wave basis set with an energy cutoff 270 eV. As for the
Brillouin-zone sampling, we use the Monkhorst-Pack mesh with 13 13  3 k-points, which has
been tested to be well converged. The self-consistent convergence accuracy is set at 5  10
6
eV
per atom, the convergence criterion for the force between atoms is 0.01 eV per Å and the total
stresses are below 0.02 eV/ Å 3.
Table List
Table S1. The lattice parameters of the bulk GeSe. Length is in the unit of Å.
Table S2. The values and types of the energy band gaps (Eg) of the bulk GeSe and GeSe
monolayer given by theoretical and experimental researches.
Table S3. The optimized lattice parameters of the GeSe monolayer. Length is in the unit of Å.
Table S1 The lattice parameters of the bulk GeSe. Length is in the unit of Å.
Method
a
b
c
GGA-PBE
4.49
3.78
10.89
GGA-RPBE
4.83
3.79
14.69
GGA-PW91
4.41
3.84
10.82
GGA-WC
4.23
3.86
10.65
GGA-PBESOL
4.21
3.85
10.60
Exp.4
4.40
3.85
10.82
Exp.5
4.39
3.83
10.82
Exp.6
4.386
3.84
10.84
Exp.7
4.37
3.81
10.78
Exp.8
4.39
3.83
10.84
Theo.9(EOLCAO)
4.38
3.82
10.79
Theo.10(LDA)
4.29
3.74
10.58
Theo.11(GGA)
4.41
3.86
10.86
Theo. 12(HSE06)
4.38
3.95
——
Present
calculation
The superscripts “i” in the table represent the references [i] below.
Table S2 The values and types of the energy band gaps (Eg) of the bulk GeSe and GeSe monolayer
given by theoretical and experimental researches. Energy is in the unit of eV. “I” in the bracket
represents indirect band gap, “D” represents direct band gap and “U” represents unspecified type.
GeSe monolayer
Bulk GeSe
Calculation method
Eg
Calculation method
Eg
GGA-PBE
1.129(D)
GGA-RPBE
1.602 (D)
GGA-RPBE
1.802(I)
GGA-PBE
0.848 (D)
GGA-PW91
1.16(D)
GGA-PW91
0.866 (I)
GGA-WC
0.942(D)
GGA-WC
0.425 (I)
GGA-PBESOL
0.881(D)
GGA-PBESOL
0.387 (I)
HSE06
1.771(I)
HSE06
1.291 (I)
1.818(D)
1.355 (D)
Theo.11 (HSE06)
1.73 (D)
Theo.6(LDA)
0.35 (I)
Theo.11 (GGA)
1.22 (D)
Theo.9(EOLCAO)
1.5 (D)
Theo.10(GGA)
1.08 (I)
Exp.7
1.08 (U)
1.14(I)-1.24(D)
Exp.8
1.24 (I)
Exp.10
1.07-1.29 (U)
Exp.12
1.29 (U)
Exp.13
1.1 (I)
The superscripts “i” in the table represent the references [i] below.
Table S3 The optimized lattice parameters of the GeSe monolayer. Length is in the unit of Å.
Method
a
B
c
GGA-PBE
4.18
3.90
21.62
GGA-RPBE
4.83
3.78
21.82
GGA-WC
4.01
3.96
20.99
GGA-PBESOL
3.99
3.96
20.85
GGA-PW91
4.157
3.961
19.93
References
[1]M. D. Segall, P. J. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clark, and M. C.
Payne, J. Phys. Condens. Matter 14, 2717 (2002).
[2]J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).
[3]T. H. Fischer, and J. Almlof, J. Phys. Chem. 96, 9768 (1992).
[4]R.W. G. Wyckoff, Crystal Structures, Second edition. Interscience Publishers, NewYork. 1963, 1, 85-237.
[5]D. S. Kyriakos, and A. N. Anagnostopoulos, J. Appl. Phys. 58(10), 3917 (1985).
[6]H. C. Hsueh, H.Vass, S. J. Clark, G. J. Ackland, and J. Crain, Phys Rev. B 51 (23), 16750 (1995).
[7]D. D. Vaughn II, R. J. Patel, M. A. Hickner, and R. E. Schaak, J. Am. Chem. Soc. 132, 15170 (2010).
[8]B. Mukherjee, Y. Q. Cai, H. R. Tan, Y. P. Feng, E. S. Tok, and C. H. Sow, ACS Appl. Mater. Interfaces 5, 9594
(2013).
[9]F. M. Gashimzade, D. G. Guliev, D. A. Guseinova, and V. Y. Shteinshrayber, J. Phys.:Condens. Matrer 4, 1081
(1992).
[10]L. Makinistian and E. A. Albanesi, J. Phys.: Condens. Matter 19, 186211 (2007).
[11]A. K. Singh and R. G. Hennig, Appl. Phys. Lett. 105, 042103 (2014).
[12]G. Valiukonis, D. A. Guseinova, G. Krivaite, and A. Sileika, Phys. Status Solidi b 135, 299 (1986).
[13]W. H. Strehlow and E. Cook, J. Phys. Chem. Ref. Data 2, 163, 173 (1973).
Figure List
Figure S1. Energy band structure and PDOS of the GeSe monolayer calculated at the level of
GGA (PW91).
Figure S2. Energy band structure and PDOS of the bulk GeSe calculated at the level of GGA.
Figure S3. The side views of the HOMO of the bulk GeSe (a) and monolayer GeSe (b) with the
isosurface value 0.03eÅ-3.
Figure S4. Electronic band structures of the GeSe monolayer under uniaxial strain of -3% (a), and
tensions of 3% (b), and 8% (c) along y direction. The horizontal dash line represents the Fermi
level. The black arrows point from the VBM to CBM.
Figure S5. Electronic band structures of the GeSe monolayer under biaxial strain of -3% (a), 3%
(b), and 9% (c) along x and y axes. The horizontal dash line represents the Fermi level. The black
arrows point from the VBM to CBM.
Figure S6 Variations of energy band gap of GeSe monolayer under tension (positive value) and
compression (negative value) along x (a), y (b) and both x and y axes (biaxial strain) (c).
Four strain zones with direct band gap are identified (in yellow color), and the other six strain
zones with indirect band gap are identified (in green color).
6
Se-S
Se-p
Ge-S
Ge-p
Total
E-EFermi (eV)
0
-6
-12





0
2
4
DOS (a.u.)
6
Figure S1 Energy band structure and PDOS of the GeSe monolayer calculated at the level of
GGA.
E-EFermi (eV)
5
0
-5
Se-S
Se-p
Ge-S
Ge-p
Total
-10
-15




S
X
U
R 0
5
DOS (a.u.)
Figure S2 Energy band structure and PDOS of the bulk GeSe calculated at the level of GGA.
10
Figure S3. The side views of the HOMO of the bulk GeSe (a) and monolayer GeSe (b) with the
iso-surface value 0.03eÅ-3. It’s easy to see from above that the geometrical structures of
monolayer GeSe are different, and there are obvious interactions between the most neighboring
monolayers in the bulk GeSe.
(b) 
E-EFermi (eV)
(a) 
4
(c) 
2
C
C
D
0
0
A
1
B
A
-2

 S


  S
 
  S  
Figure S4. Electronic band structures of the GeSe monolayer under uniaxial strain of -3% (a), and
tensions of 3% (b), and 8% (c) along y direction. The horizontal dash line represents the Fermi
level. The arrows point from the VBM to CBM. The direct/indirect nature of the band gap is the
result of the competition among the energies of near-band-edge states A-D.
E-EFermi (eV)
4
(a) 
(b) 
(c) 
C
C
2
D
0
E
A
A
0
1
-2
  S 

  S  
  S  
Figure S5. Electronic band structures of the GeSe monolayer under biaxial strain of -3% (a), 3%
(b), and 9% (c) along x and y axes. The horizontal dash line represents the Fermi level. The arrows
point from the VBM to CBM. The direct/indirect nature of the band gap is the result of the
competition among the energies of near-band-edge states (A, C-E).
1.5
(a) along x axis
1.0
0.5
E-E Fermi (eV)
0.0
1.5
1.0
(b) along y axis
Gap
0.5
0.0
1.5
(c) along x and y axes
1.0
Direct
Indirect
0.5
0.0
-9%
-6%
-3%
0%

3%
6%
9%
Figure S6 Variations of energy band gap of GeSe monolayer under tension (positive value) and
compression (negative value) along x (a), y (b) and both x and y axes (biaxial strain) (c).
Four strain zones with direct band gap are identified (in yellow color), and the other six strain
zones with indirect band gap are identified (in green color).