First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions

doi:10.1007/s11467-010-0133-4

Front Phys Chin

2010, Vol. 5

Issue (4) : 369-379 https://doi.org/10.1007/s11467-010-0133-4

REVIEW ARTICLE

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

Download: PDF(517 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

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.

Keywords STM simulation non-equilibrium Green’s function Wannier function

Corresponding Author(s): null,Email:Haiping.Lin@liverpool.ac.uk; HOFER Werner A.,Email:whofer@liverpool.ac.uk

Issue Date: 05 December 2010

Cite this article:

Haiping LIN (林海平),Janosch M. C. RAUBA,Kristian S. THYGESEN, et al. First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions[J]. Front Phys Chin, 2010, 5(4): 369-379.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-010-0133-4
https://academic.hep.com.cn/fop/EN/Y2010/V5/I4/369

1	G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Phys. Rev. Lett. , 1982, 49: 57 doi: 10.1103/PhysRevLett.49.57
2	G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Phys. Rev. Lett. , 1983, 50: 120 doi: 10.1103/PhysRevLett.50.120
3	J. A. Heinrich, C. P. Lutz, J. A. Gupta, and D. M. Eigler, Science , 2002, 298: 1381 doi: 10.1126/science.1076768
4	C. Joachim, J. K. Gimzewski, and A. Aviram, Nature , 2000, 408: 541 doi: 10.1038/35046000
5	H. C. Manoharan, C. P. Lutz, and D. M. Eigler, Nature , 2000, 403: 512 doi: 10.1038/35000508
6	S.-W. Hla, L. Bartels, G. Meyer, and K.-H. Rieder, Phys. Rev. Lett. , 2000, 85: 2777 doi: 10.1103/PhysRevLett.85.2777
7	S.-W. Hla and K.-H. Rieder, Ann. Rev. Phys. Chem. , 2003, 54: 307 doi: 10.1146/annurev.physchem.54.011002.103852
8	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
9	J. Tersoff and D. R. Hamann, Phys. Rev. B , 1981, 31: 805 doi: 10.1103/PhysRevB.31.805
10	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
12	J. Bardeen, Phys. Rev. Lett. , 1961, 6: 57 doi: 10.1103/PhysRevLett.6.57
13	W. A. Hofer and J. Redinger, Surf. Sci. , 2000, 447: 51 doi: 10.1016/S0039-6028(99)01053-5
14	K. S. Thygesen and K. W. Jacobsen, Chem. Phys. , 2005, 319: 111 doi: 10.1016/j.chemphys.2005.05.032
15	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
18	G. H. Wannier, Phys. Rev. , 1937, 52: 191 doi: 10.1103/PhysRev.52.191
19	N. Marzari and D. Vanderbilt, Phys. Rev. B , 1997, 56: 12847 doi: 10.1103/PhysRevB.56.12847
20	K. S. Thygesen, L. B. Hansen, and K. W. Jacobsen, Phys. Rev. Lett. , 2005, 94: 026405 doi: 10.1103/PhysRevLett.94.026405
21	K. S. Thygesen, L. B. Hansen, and K. W. Jacobsen, Phys. Rev. B , 2005, 72: 125119 doi: 10.1103/PhysRevB.72.125119
22	K. S. Thygesen, Phys. Rev. B , 2006, 73: 035309 doi: 10.1103/PhysRevB.73.035309
23	C. J. Chen, Introduction to Scanning Tunnelling Microscopy, New York: Oxford University Press, 1993
24	S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge: Cambridge University Press, 1995
25	M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Phys. Rev. B , 1985, 31: 6207 doi: 10.1103/PhysRevB.31.6207
26	K. Palotás and W. A. Hofer, J. Phys.: Condens. Matter , 2005, 17: 2705 doi: 10.1088/0953-8984/17/17/019
27	A. S. Foster and W. A. Hofer, Scanning Probe Microscopy, Spring Series in NanoScience and Technology, Springer , 2006
28	W. A. Hofer and A. J. Fisher, Phys. Rev. Lett. , 2003, 91: 036803 doi: 10.1103/PhysRevLett.91.036803
29	W. A. Hofer and A. Garcia-Lekue, Phys. Rev. B , 2005, 71: 085401 doi: 10.1103/PhysRevB.71.085401
30	W. A. Hofer, A. Garcia-Lekue, and H. Brune, Chem. Phys. Lett. , 2004, 397: 354 doi: 10.1016/j.cplett.2004.08.110
31	C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James, Journal of Physics C , 1971, 4: 916
32	T. E. Feuchtwang, Phys. Rev. B , 1974, B10: 4135 doi: 10.1103/PhysRevB.10.4135
33	T. E. Feuchtwang, Phys. Rev. B , 1974, 10: 4121 doi: 10.1103/PhysRevB.10.4121
34	T. E. Feuchtwang, Phys. Rev. B , 1976, 13: 517 doi: 10.1103/PhysRevB.13.517
35	Y. Meir and N. S. Wingreen, Phys. Rev. Lett. , 1992, 68: 2512 doi: 10.1103/PhysRevLett.68.2512
36	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
49	G. Kresse and J. Hafner, Phys. Rev. B , 1993, 47: 558 doi: 10.1103/PhysRevB.47.558
50	G. Kresse and J. Hafner, Phys. Rev. B , 1994, 49: 14251 doi: 10.1103/PhysRevB.49.14251
51	G. Kresse and J. Furthmüller, Comput. Mater. Sci. , 1996, 6: 15 doi: 10.1016/0927-0256(96)00008-0
52	G. Kresse and J. Furthmüller, Phys. Rev. B , 1996, 54: 11169 doi: 10.1103/PhysRevB.54.11169
53	J. J. Mortensen, L. B. Hansen, and K. W. Jacobsen, Phys. Rev. B , 2005, 71: 035109 doi: 10.1103/PhysRevB.71.035109
54	J. Enkovaara, , J. Phys.: Condens. Matter (in press)
55	W. A. Hofer, Progr. Surf. Sci. , 2003, 71: 147 doi: 10.1016/S0079-6816(03)00005-4

[1]	Junbo Zhu (竺俊博),Zhu Chen (陈竹),Biao Wu (吴飙). Construction of maximally localized Wannier functions[J]. Front. Phys. , 2017, 12(5): 127102-.
[2]	Jing NING (宁静), Xin SHEN (沈昕), Zi-yong SHEN (申自勇), Xing-yu ZHAO (赵兴钰), Shi-min HOU (侯士敏). First-principles calculation on the conductance of ruthenium-quasi cumulene-ruthenium molecular junctions[J]. Front Phys Chin, 2009, 4(3): 398-402.

Viewed

Full text

Abstract

Cited

Shared

Discussed