Electronic Supplementary Information

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1 Electronic Supplementary Material (ESI) for Nanoscale. This journal is The Royal Society of Chemistry 2016 Electronic Supplementary Information Two-dimensional BX (X=P, As, Sb) Semiconductors with Mobilities Approaching Graphene Meiqiu Xie, a Shengli Zhang, a Bo Cai, a Zhen Zhu, b Yousheng Zou a and Haibo Zeng a * a Institute of Optoelectronics and Nanomaterials, Jiangsu Key Laboratory of Advanced Micro & Nano Materials and Technology, College of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing , China b Materials Department, University of California, Santa Barbara, CA 93106, USA * zeng.haibo@njust.edu.cn These authors contributed equally to this work.

2 S1. Stability (Cohesive energy and phonon dispersion) Table S1. Structural and electronic properties of monolayer BX (X=P, As, and Sb) sheets. Fig. S1 Electronic band structures of monolayer (a) BP, (b) BAs, (c) BSb; the red star lines base on PBE level while the green ones are for HSE level. The horizontal dotted line indicates the Fermi level. Fig. S2 (a) Partial density of states (PDOS) of B and P atoms around the Fermi level. The vertical dotted line indicates the Fermi level. (b) Electronic profiles for VBM (up) and CBM (down) from the top and side views, respectively, with an iso-value of eå -3. Fig. S3 Electronic band structures of monolayer BSb base on PBE+SOC (a), and HSE+SOC (b) level, respectively. The horizontal dotted line indicates the Fermi level. Fig. S4 The partial data about VBM,VBM+1, CBM, and CBM+1 of monolayer BSb are offered based on PBE+SOC (a), and HSE+SOC (b) level, respectively. Fig. S5 Electronic band structures of monolayer (a) BP, (b) BAs, (c) BSb sheet in the orthogonal supercell, K point refers to the high symmetry in the first Brillouin zone of rhombus primitive cell. The horizontal dotted line indicates the Fermi level. Fig. S6 Relative error in the deformation potential (DP) constant. Band energies of the VBM and CBM of monolayer BP (a), (b), (c), and (d), monolayer BP with respect to the vacuum energy as a function of lattice dilation. The fitting curves are showed in red solid lines. Insets present the standard errors of the fitted slope, which corresponds to the DP constant. Fig. S7 Relative error in the DP constant. Band energies of the VBM and CBM of monolayer BAs (a), (b), (c), and (d), monolayer BAs with respect to the vacuum energy as a function of lattice dilation. The fitting curves are showed in red solid lines. Insets present the standard errors of the fitted slope, which corresponds to the DP constant. Fig. S8 Relative error in the DP constant. Band energies of the VBM and CBM of monolayer BSb (a), (b), (c), and (d), monolayer BSb with respect to the vacuum energy as a function of lattice dilation. The fitting curves are showed in red solid lines. 1

3 Insets present the standard errors of the fitted slope, which corresponds to the DP constant. Fig. S9 Calculated monolayer (a) BP, (b) BAs, (c) BSb sheet carrier mobility as a function of temperature. S1 Stability (Cohesive energy and phonon dispersion) Thermodynamic stability of 2D BX (X=P, As, and Sb) monolayers is evaluated by cohesive energy. Cohesive energies (E coh ) per pair of atoms, as shown in Table S1, are defined by performing the expression E coh (BX) = E BX E B E X (S1) where E BX is the total energy per B-X pair of the relaxed hexagonal configuration; E B and E X are the total energies of free atoms B and X with respect to nonmagetic state (X stand for P, As, and Sb herein). The cohsesive energy of the one-atom-thick BX have been reported, toghther with graphene and silicene for comparsion. 1 According to DFT calculation, the numerical value order of BX monolayers is in good agreement with the above-mentioned result. Whether imaginary frequency or not in phonon dispersion computations, which can be a norm to examine the structural instability. From the Fig. 1c, no soft modes are contained in the single layer boron compounds (BP, BAs and BSb), representing the dynamic stability. The highest phonon frequency of BX monolayers in sequentially are about , 838.9, and cm -1, which are much higher than the highest frequency of 580 cm -1 in silicene, cm -1 in MoS 2 monolayer, 3 indicating robust B- X bonds in BX monolayers. References 1 H. L. Zhuang and R. G. Hennig, Appl. Phys. Lett., 2012, 101, S. Cahangirov, M. Topsakal, E. Aktürk, H. Şahin and S. Ciraci, Phys. Rev. Lett., 2009, 102, A. Molina-Sanchez and L. Wirtz, Phys. Rev. B, 2011, 84,

4 Table S1 Structural and electronic properties of monolayer BX (X=P, As, and Sb) sheets a BX (X=P, As, Sb) monolayers Models a 1 (Å) d (Å) E coh (ev/atom) E PBE (ev) E HSE (ev) BP BAs BSb a a 1 and d are in-plane unit vectors and bond length defined in rhombus primitive cell, see Fig. 1. The cohesive energies E coh are computed in reference to the spin-polarized B and X atoms. E PBE and E HSE are band gap calculated by performing PBE and HSE06 functional, respectively. Fig. S1 Electronic band structures of monolayer (a) BP, (b) BAs, (c) BSb; the red lines base on PBE level while the green ones are for HSE level. The horizontal dotted line indicates the Fermi level. Fig. S2 (a) Partial density of states (PDOS) of B and P atoms around the Fermi level. The vertical dotted line indicates the Fermi level. (b) Electronic profiles for VBM (up) and CBM (down) from the top and side views, respectively, with an iso-value of eå -3. 3

5 Fig. S3 Electronic band structures of monolayer BSb base on PBE+SOC (a), and HSE+SOC (b) level, respectively. The horizontal dotted line indicates the Fermi level. Fig. S4 The partial data about VBM,VBM+1, CBM, and CBM+1 of monolayer BSb are offered based on PBE+SOC (a), and HSE+SOC (b) level, respectively. 4

6 Fig. S5 Electronic band structures of monolayer (a) BP, (b) BAs, (c) BSb sheet in the orthogonal supercell, K point refers to the high symmetry in the first Brillouin zone of rhombus primitive cell. The horizontal dotted line indicates the Fermi level. Fig. S6 Relative error in the deformation potential (DP) constant. Band energies of the VBM and CBM of monolayer BP (a), (b), (c), and (d), monolayer BP with respect to the vacuum energy as a function of lattice dilation. The fitting curves are showed in red solid lines. Insets present the standard errors of the fitted slope, which corresponds to the DP constant. 5

7 Fig. S7 Relative error in the DP constant. Band energies of the VBM and CBM of monolayer BAs (a), (b), (c), and (d), monolayer BAs with respect to the vacuum energy as a function of lattice dilation. The fitting curves are showed in red solid lines. Insets present the standard errors of the fitted slope, which corresponds to the DP constant. Fig. S8 Relative error in the DP constant. Band energies of the VBM and CBM of monolayer BSb 6

8 (a), (b), (c), and (d), monolayer BSb with respect to the vacuum energy as a function of lattice dilation. The fitting curves are showed in red solid lines. Insets present the standard errors of the fitted slope, which corresponds to the DP constant. Fig. S9 Calculated monolayer (a) BP, (b) BAs, (c) BSb sheet carrier mobility as a function of temperature. 7