First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions
First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions
Haiping LIN (林海平)1(), Janosch M. C. RAUBA2, Kristian S. THYGESEN2, Karsten W. JACOBSEN2, Michelle Y. SIMMONS3, Werner A. HOFER1()
1. Surface Science Research Centre, The University of Liverpool, Liverpool, L69 3BX, UK; 2. Center for Atomic-scale Materials Design, Technical University of Denmark, DK-2800 Lyngby, Denmark; 3. Centre of Quantum Computer Technology, School of Physics, The University of New South Wales, Sydney NSW 2052, Australia
The investigation of electron transport processes in nano-scale architectures plays a crucial role in the development of surface chemistry and nano-technology. Experimentally, an important driving force within this research area has been the concurrent refinements of scanning tunneling microscopy (STM) techniques. The theoretical treatment of the STM operation has traditionally been based on the Bardeen and Tersoff–Hamann methods which take as input the single-particle wave functions and eigenvalues obtained from finite cluster or slabs models of the surface-tip interface. Here, we present a novel STM simulation scheme based on non-equilibrium Green’s functions (NEGF) and Wannier functions which is both accurate and very efficient. The main novelty of the scheme compared to the Bardeen and Tersoff–Hamann approaches is that the coupling to the infinite (macroscopic) electrodes is taken into account. As an illustrating example we apply the NEGF-STM method to the Si(001)-(2×1):H surface with sub-surface P doping and discuss the results in comparison to the Bardeen and Tersoff–Hamann methods.
Corresponding Author(s):
null,Email:Haiping.Lin@liverpool.ac.uk; HOFER Werner A.,Email:whofer@liverpool.ac.uk
引用本文:
. First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions[J]. Frontiers of Physics in China, 2010, 5(4): 369-379.
Haiping LIN (林海平), Janosch M. C. RAUBA, Kristian S. THYGESEN, Karsten W. JACOBSEN, Michelle Y. SIMMONS, Werner A. HOFER. First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions. Front Phys Chin, 2010, 5(4): 369-379.
M. Fuechsle, S. Mahapatra, F. A. Zwanenburg, M. Friesen, M. A. Eriksson, and M. Y. Simmons, Nature Nanotechnology , 2010, 5: 502 doi: 10.1038/nnano.2010.95
J. Tersoff and D. R. Hamann, Phys. Rev. Lett. , 1985, 50: 1988
11
W. A. Hofer, G. Ritz, W. Hebenstreit, M. Schmid, P. Varga, J. Redinger, and R. Podloucky, Surf. Sci. Lett. , 1998, 405: L514 doi: 10.1016/S0039-6028(98)00140-X
W. A. Hofer, A. S. Foster, and A. L. Shluger, Rev. Mod. Phys. , 2003, 75: 1287 doi: 10.1103/RevModPhys.75.1287
16
Z. T. Deng, H. Lin, W. Ji, L. Gao, X. Lin, Z. H. Cheng, X. B. He, J. L. Lu, D. X. Shi, W. A. Hofer, and H. J. Gao, Phys. Rev. Lett. , 2006, 96: 156102 doi: 10.1103/PhysRevLett.96.156102
17
A. Calzolari, N. Marzari, I. Souza, and M. B. Nardelli, Phys. Rev. B , 2004, 69: 035108 doi: 10.1103/PhysRevB.69.035108
H. Hauge and A. P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer Series in Solid-State Physics, Springer , 1996
37
F. Flores, F. Guinea, C. Tejedor, and E. Louis, Phys. Rev. B , 1983, 28: 4397 doi: 10.1103/PhysRevB.28.4397
38
K. Flensberg and H. Bruus, Many-Body Quantum Theory in Condensed Matter Physics, Chapter 8, New York: Oxford University Press, 2004
39
S. Garcia-Gil, A. Garcia, N. Lorente, and P. Ordejon, Phys. Rev. B , 2009, 79: 075441 doi: 10.1103/PhysRevB.79.075441
40
L. Liu, J. Yu, and J. W. Lyding, Appl. Phys. Lett. , 2001, 78: 386 doi: 10.1063/1.1339260
41
L. Liu, J. Yu, and J. W. Lyding, IEEE Trans. Nanotechnol. , 2002, 1: 176 doi: 10.1109/TNANO.2002.807391
42
G. W. Brown, H. Grube, and M. E. Hawley, Phys. Rev. B , 2004, 70: 121301 doi: 10.1103/PhysRevB.70.121301
43
L. Oberbeck, N. J. Curson, T. Hallam, M. Y. Simmons, and R. G. Clark, Thin Solid Films , 2004, 464: 23 doi: 10.1016/j.tsf.2004.05.118
44
J. W. Lyding, T. C. Shen, J. S. Hubacek, J. R. Tucker, and G. C. Abeln, Appl. Phys. Lett. , 1994, 64: 2010 doi: 10.1063/1.111722
45
S. R. Schofield, N. J. Curson, M. Y. Simmons, F. J. Rueβ, T. Hallam, L. Oberbeck, and R. G. Clark, Phys. Rev. Lett. , 2003, 91: 136104 doi: 10.1103/PhysRevLett.91.136104
46
F. J. Ruess, L. Oberbeck, M. Y. Simmons, K. E. J. Goh, A. R. Hamilton, T. Hallam, S. R. Schofield, N. J. Curson, and R. G. Clark, Nano Lett. , 2004, 4: 1969 doi: 10.1021/nl048808v
47
A. Fuhrer, M. Fchsle, T. C. G. Reusch, B. Weber, and M. Y. Simmons, Nano Lett. , 2009, 9: 707 doi: 10.1021/nl803196f
48
J. L. O’Brien, S. R. Schofield, M. Y. Simmons, R. G. Clark, A. S. Dzurak, N. J. Curson, B. E. Kane, N. S. McAlpine, M. E. Hawley, and G. W. Brown, Phys. Rev. B , 2001, 64: 161401(R) doi: 10.1103/PhysRevB.64.161401