Tunable electronic properties of silicon nanowires under strain and electric biasAlexis Nduwimana and Xiao-Qian Wang Citation: AIP Advances 4, 077122 (2014); doi: 10.1063/1.4890674 View online: http://dx.doi.org/10.1063/1.4890674 View Table of Contents: http://scitation.aip.org/content/aip/journal/adva/4/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Tunable optical and electronic properties of Si nanowires by electric bias J. Appl. Phys. 109, 083106 (2011); 10.1063/1.3576100 Vibrational and thermal properties of small diameter silicon nanowires J. Appl. Phys. 108, 063702 (2010); 10.1063/1.3481406 Electronic properties of strained Si/Ge core-shell nanowires Appl. Phys. Lett. 96, 143119 (2010); 10.1063/1.3389495 Silicon nanowire n -type metal-oxide-semiconductor field-effect transistors and single-electron transistors at roomtemperature under uniaxial tensile strain J. Appl. Phys. 105, 084514 (2009); 10.1063/1.3115448 Uniaxial-stress effects on electronic properties of silicon carbide nanowires Appl. Phys. Lett. 89, 023104 (2006); 10.1063/1.2221388

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/

Downloaded to IP: 209.172.228.248 On: Sun, 23 Nov 2014 23:07:39

AIP ADVANCES 4, 077122 (2014)

Tunable electronic properties of silicon nanowires understrain and electric bias

Alexis Nduwimana1,2 and Xiao-Qian Wang1,a

1Department of Physics and Center for Functional Nanoscale Materials, Clark AtlantaUniversity, Atlanta, Georgia 30314, USA2Georgia Perimeter College, Decatur, Georgia 30034, USA

(Received 12 June 2014; accepted 9 July 2014; published online 17 July 2014)

The electronic structure characteristics of silicon nanowires under strain and electricbias are studied using first-principles density functional theory. The unique wire-like structure leads to distinct spatial distribution of carriers, which can be tailoredby applying tensile and compressive strains, as well as by an electric bias. Ourresults indicate that the combined effect of strain and electric bias leads to tunableelectronic structures that can be used for piezo-electric devices. C© 2014 Author(s). Allarticle content, except where otherwise noted, is licensed under a Creative CommonsAttribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4890674]

Semiconducting nanowires (NWs) are basic building blocks for the function and integration ofnanoscale devices such as nanoswitches, single electron transistors, optoelectronic units, sensors, andsolar cells.1–10 Silicon nanowires (SiNWs) are prototype semiconducting wires that have attracteda great deal of attention.11 They have been found to have more advantageous catalytic propertiesthan palladium or gold.12 SiNWs have the potential to improve the storage capacity for the lithiumion-battery anode.13 SiNW based solar cells are shown to have high efficiency.14 An in-depthunderstanding on tailoring the electronic properties of SiNWs is thus of importance to technologicaladvances.

External strain has an important effect on the electronic structures of low-dimensional materials.Combined with an electric bias, they have a profound influence on the properties of materials atthe nanoscale level. Strain and electric bias induce shifts in the intrinsic interatomic distance. Theresulting structure deformation significantly modifies the electronic and optical properties of thenanomaterials. The impact of tensile and compressive strain on SiNWs is fundamentally importantsince the strain can yield nanostructures with novel properties, as nanomaterials respond to straindifferently than their bulk counterparts.15–18 A longitudinal electric bias modulates the band gap,while a transverse electric field leads to a transformation from an indirect band gap to a direct gap,making the NWs suitable for optoelectronic applications.19

Despite intense studies of the effect of strain and the electric bias, this concerted effect is notwell understood. Encouraged by recent experimental results on the tailoring of electronic propertiesin SiNWS,20 we report on calculation results based on first-principles density functional theory(DFT) for the effect of an external electric field and mechanical strain on SiNWs as well as Si/Geand Ge/Si core-shell structured NWs. The combination leads to an increase in the piezoresistance ofSiNWs and core-shells. The resulting tunable piezoelectric effect can potentially usher the creationof improved devices. For instance, low gain devices could be used as conventional piezoresistivesensors, while high gain devices could be used as powerful force-activated mechanical switches andmechanical/electric comparators. Similar result were accomplished for SiNWs in [100] directionwhere the piezoelectric coefficient was reported to be 20 times higher than the bulk.21 The piezore-sistance degrades from giant to bulk silicon values as the backgate bias is increased beyond a certainthreshold.22, 23

aElectronic mail: xwang@cau.edu

2158-3226/2014/4(7)/077122/7 C© Author(s) 20144, 077122-1

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/

Downloaded to IP: 209.172.228.248 On: Sun, 23 Nov 2014 23:07:39

077122-2 A. Nduwimana and X.-Q. Wang AIP Advances 4, 077122 (2014)

FIG. 1. Ball-and-stick model of representative SiNW (top left panel), Si/Ge core-shell (top right panel), and the side view ofthe SiNW, respectively. Silicon, germanium, and hydrogen atoms are colored with orange, green, and white, respectively.

We have examined SiNWs along the [110] direction as prototype NW systems as well as theSi/Ge and Ge/Si core-shell structures. The SiNWs were constructed from diamond structure witha roughly cylindrical shape along with hydrogen passivation on the surface. Depicted in Fig. 1 isthe ball-and-stick model of the prototype NW studied. The NW has a diameter of 1.74 nm with 42silicon atoms and 20 hydrogen atoms in the unit cell. Our first-principles calculations are based onDFT with the Vasko-Wilk-Nusair local density approximation (LDA) as implemented in DMol3.24

The calculation was done using an all-electrons potential with double numerical plus polarization(DNP) as the basis set. A 15 Åsupercell was used to eliminate the interaction with neighboring wires.The energy was allowed to converge up to 10−5 eV. Nanowires were optimized using the Monkhorstsampling of 1 × 1 × 11 k-point grid. We used an energy convergence criterion of 5 × 10−4 eV.A 3% compression or extension was applied to the NWs. The amount of strain was selected sinceit demonstrates a notable change on the electronic structure.28 The compressive and tensile strainwere applied through decreasing and increasing the lattice constant along the wire, respectively. Anelectric field of 0.8 V/Åwas applied in the transverse direction. The amount of electric bias wasshown to reveal appropriate changes in the electronic structure while not transforming to a metallicstate (for large bias). It is known that the application of sawtooth electric field in a periodic systemcan induce an artifact; which can be rectified with appropriate large vacuum.18, 25 We have carefullytested the convergence of our results with respect to vacuum used.

Shown in Fig. 2 are the calculated band structures of near band gap states of the [110] SiNWunder a combination of strain and electric bias. The electric field is applied in the direction

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/

Downloaded to IP: 209.172.228.248 On: Sun, 23 Nov 2014 23:07:39

077122-3 A. Nduwimana and X.-Q. Wang AIP Advances 4, 077122 (2014)

FIG. 2. Calculated band structures of SiNW for the 3% compressed SiNW (left panels indicated by →←), pristine SiNW(middle panels) and 3% strained SiNW(right panels indicated by ←→ ), respectively. The first and second row illustratesthe corresponding band structures without and with an electric bias ε, respectively.

perpendicular to the SiNW. As seen in Fig. 2, the effect of strain on the band gap is consistentwith that of SiNWs along [111].15 With compressive and tensile strain, bands near the band edgeL shift up and down, respectively. There is a notable change in the dispersion of the valence andconduction bands in the proximity of the � point, resulting in a decrease of the effective mass forboth compressive and tensile strain. The effective mass of the VBM for a pristine NWs was found tobe 0.41 me where me is the mass of an electron. When a compressive or tensile strain was applied, theeffective mass changed to 0.15, and 0.31 me respectively. Under a compressive strain, the effectivemass decreased from 1.20 to 0.40 me. The strain induced change in the effective mass is attributedto the overlap modification for atomic orbitals. When the NW is compressed, the magnitude ofthe overlap increases, leading to a reduced effective mass. This modification of the effective massimpacts the electric transport of SiNWs. These results are similar to those of SiNWs along [111]directions where the light hole effective mass decreases under stress and increases when under tensilestrain.15 It is worth noting that the changes are greater for SiNWs along [110] than those in [111]direction.

With the application of a transverse electric bias perpendicular to the NW direction, there isa notable reduction in the band gap. This is attributed to the fact that the electric field potential(proportional to the carrier charge) has opposite effects on electrons and holes. As a results, theconduction bands energy lowers while the energy of valence bands increases.

Tuning the band gap is desirable for device applications. It appears that there is a downward shiftof valence states and a modification of the conduction and valence band dispersion. In particular,a reduction in the effective mass near the � point is better achieved with the application of bothcompressive strain and electric field bias. The above effects are concerted whereby the effectivemass near the � point reduces significantly as a compressive strain is applied. The downward shiftof valence states is more pronounced, leading to a semi-metallic state. For the pristine SiNW, an

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/

Downloaded to IP: 209.172.228.248 On: Sun, 23 Nov 2014 23:07:39

077122-4 A. Nduwimana and X.-Q. Wang AIP Advances 4, 077122 (2014)

FIG. 3. Extracted charge density of the VBM and CBM for SiNW without and with an electric bias ε, respectively. The topand bottom panels are for NW under compressive and tensile strain, respectively.

electric bias reduces the effective mass of both the valence band maximum (VBM) and conductionband minimum (CBM). The combination of tensile (or compresssive) strain and electric bias hasthe effect of increasing the electron effective mass while educing hole effective mass. The effectivemass for the VBM increased from 0.15 to 0.40 me when a transverse electric bias was applied to aNW under a compressive strain. On the other hand, the CBM effective mass decreased from 0.40 to0.30 me.

We illustrate in Fig. 3, the charge density of SiNWs under compressive or tensile strain witha transverse electric field. As can be seen from Fig. 3, the charge density of the VBM displays astrong shell characteristic as compression is applied to the NW while the converse happens duringa contraction. In fact,the effect of a strain can be modeled as a linear potential γ R with γ being lessand greater than zero for a contraction and extension, respectively.15 For a SiNW under compression,the strain potential is minimum at the shell (γ < 0). Therefore, the charge density is localized at theshell for compressive strain. On the other hand, NWs under a tensile strain have their charge densitymoving toward the core.

With the application of an electric field directed toward the [11̄0] direction, the charge densityof the VBM is shifted toward the [11̄0] while the CBM’s charge is shifted toward [1̄10]. The shift isthe result of the linear electric potential, which has its maximum at the [11̄0] edge of the unit celland a minimum on the opposite edge. The combination of an electric field and a compressive strainresults in the VBM’s charge density localized on the shell near the [11̄0] edge and a conduction bandshifted to the [11̄0] shell. The combination of an electric field and a tensile extension moves theVBM charge density toward the [11̄0] edge but with a residual central charge density. The charge ofthe CBM moves to the [1̄10] edge with a significant central charge density.

To facilitate a better understanding of the electric field for heterostructure, we investigated Ge/Siand Si/Ge core-shell nanowires electronic. Shown in Fig. 4 is the band structure of Si/Ge and Ge/Sicore-shell NW of the same diameter as the pristine SiNW. The core has 16 atoms and a 1.0 nm

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/

Downloaded to IP: 209.172.228.248 On: Sun, 23 Nov 2014 23:07:39

077122-5 A. Nduwimana and X.-Q. Wang AIP Advances 4, 077122 (2014)

FIG. 4. Calculated band structures of Ge/Si and Si/Ge core-shell and the corresponding structures with an electric bias (ε)on left and right panels, respectively. The Ge/Si and Si/Ge core-shell band structures display similar behavior as SiNWs witha compressive and tensile strain, respectively.

diameter, while the shell has 26 atoms and 0.3 nm thickness. The effective mass of valence bandand conduction band is higher for Si/Ge core-shell than for Ge/Si core-shell. Si has a smaller latticeconstant than Ge with a 4 % mismatch. For a core-shell SiNWs, Si atoms tend to have a tensilestrain while Ge atoms displays a compression.26, 27 Comparing Fig. 2 with Fig. 4, it is evident thatthe Ge/Si core-shell has a band structure analogeous to SiNWs under compression, while Si/Ge hasa band structure comparable to SiNWs under strain.28 In spite of these similarities, the effectivemass of Si/Ge for the VBM is higher than that for SiNWs under tensile or compressive strain. Uponapplying the transverve electric field, differences arise between SiNWs and core-shells. The electricfield increases the gap by 0.3 eV for a SiNW under transverse electric field for Ge/Si core-shell. Thecorresponding electric field decreases the gap by 0.2 eV for a Si/Ge core-shell.

Shown in Fig. 5 is the charge density of the VBM and CBM for Si/Ge and Ge/Si core-shellNW. The Si/Ge core-shell charge density for the VBM is localized on the shell, while the CBMhas the charge density localized in the Si core. The reverse is observed for the Ge/Si core-shellGe/Si core-shell shows an expansive behavior (VBM localized in the core and CBM localized inthe shell), while Si/Ge resembles SiNWs under strain.27 Applying a transverse electric field to the

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/

Downloaded to IP: 209.172.228.248 On: Sun, 23 Nov 2014 23:07:39

077122-6 A. Nduwimana and X.-Q. Wang AIP Advances 4, 077122 (2014)

FIG. 5. Extracted charge density of the VBM, and CBM for Si/Ge and Ge/Si core-shells structured NWs without and withan electric bias ε, respectively.

core-shell moves the charge density of shell states toward the [11̄0] edge. Contrary to SiNWs, thecharge density of core states are not shifted.

In summary, we have performed DFT calculations of the electronic structure of SiNWs, Si/Ge,and Ge/Si core-shell in the [110] direction under tensile or compressive strain and under a transverseelectric field. SiNWs under strain modifies the effective mass of valence and conduction bands. Thistype of modification is observed for Ge/Si-core-shell as well. An electric field applied to core-shellsand SiNWs modifies the band gap and the band structure. Therefore, it is possible to tune the SiNWselectronic structure using different levels of strain and electric field. This can help change an indirectband gap to a direct one, which is useful for electronic applications. By adding a transverse electricfield, the tailoring of the band gap coupled with an increase in the effective mass is observed. Thiscan potentially increase the conductance of NWs.

This work was supported by the National Science Foundation (Grant DMR-0934142). We aregrateful to M. Y. Chou for her critical reading of the manuscript.

1 X. F. Duan, Y. Huang, Y. Cui, J. F. Wang, and C. M. Lieber, Nature 409, 66 (2001).2 W. C. Wang, C. W. Lin, H. J. Chen, C. W. Chang, J. J. Huang, M. J. Yang, B. Tjahjono, J. J. Huang, W. C. Hsu, and M. J.

Chen, ACS Appl. Mater. Interfaces 5, 9752 (2013).3 N. S. Ramgir, Y. Yang, and M. Zacharias, Small 6, 1705 (2010).4 L. J. Lauhon, M. S. Gudiksen, C. L. Wang, and C. M. Lieber, Nature 420, 57 (2002).5 Y. Cui, Z. Zhong, D. Wang, W. Wang, and C. M. Lieber, Nano Lett. 3, 149 (2003).6 A. B. Greytak, L. J. Lauhon, M. S. Gudiksen, and C. M. Lieber, Appl. Phys. Lett. 84, 4176 (2004).7 W. Lu, J. Xiang, B. P. Timko, Y. Wu, and C. M. Lieber, Proc. Natl. Acad. Sci. USA 102, 10046 (2005).8 J. Xiang, W. Lu, Y. Hu, Y. Wu, H. Yan, and C. M. Lieber, Nature 441, 489 (2006).9 Z. Wu, J. B. Neaton, and J. C. Grossman, Nano Lett. 9, 2418 (2009).

10 T. J. Kempa, R. W. Day, S.-K. Kim, H.-G. PArk, and C. M. Lieber, Energy Environ. Sci. 6, 719 (2013).11 M. W. Shao, D. D. D. Ma, and S. T. Lee, Eur. J. Inorg. Chem. 2010, 4264 (2010).12 M. W. Shao, L. Cheng, X. H. Zhang, D. D. D. Ma, and S. T. Lee, J. Am. Chem. Soc. 131, 17738 (2009).13 K. Q. Peng, J. S. Jie, W. J. Zhang, and S. T. Lee, Appl. Phys. Lett. 93, 033105 (2008).14 L. Tsakalakos, J. Balch, J. Fronheiser, and B. A. Korevaar, Appl. Phys. Lett. 91, 233117 (2007).15 A. Nduwimana and X.-Q. Wang, J. Phys. Chem. C 114, 9702 (2010).16 L. Huang, N. Lu, J. Yan, M. Y. Chou, C. Z. Wang, and K. M. Ho, J. Phys. Chem. C 112, 15683 (2008).17 A. J. Lu, R. Q. Zhang, and S. T. Lee, Appl. Phys. Lett. 91, 263107 (2007).18 R. Q. Zhang, C. Hou, N. Gao, Z. Wen, and Q. Jiang, ChemPhysChem. 12, 1302 (2011).19 R. Q. Zhang, N. Gao, J. S. Lian, and Q. Jiang, J. Appl. Phys. 109, 083106 (2011).20 P. Neuzil, C. C. Wong, and J. Reboud, Nano Lett. 10, 1248 (2010).21 V. Passi, F. Ravaux, E. Dubois, and J.-P. Raskin, 23rd IEEE International Conference (MEMS), 464 (2010).22 R. R. He and P. D. Yang, Nat. Nanotech. 1, 42 (2006).

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/

Downloaded to IP: 209.172.228.248 On: Sun, 23 Nov 2014 23:07:39

077122-7 A. Nduwimana and X.-Q. Wang AIP Advances 4, 077122 (2014)

23 J. X. Cao, X. G. Gong, and R. Q. Wu, Phys. Rev. B 75, 233302 (2007).24 B. Delley, J. Chem. Phys. 92, 508 (1990).25 K. Tang, R. Qin, J. Zhou, H. Qu, J. Zheng, R. Fei, H. Li, Q. Zheng, Z. Gao, and J. Lu, J. Chem. Phys. C 115, 9458 (2011).26 J.-S. Park, B. Ryu, C.-Y. Moon, and K. J. Chang, Nano Lett. 10, 116 (2010).27 L. Yang, R. N. Musin, X.-Q. Wang, and M. Y. Chou, Phys. Rev. B 77, 195325 (2008).28 A. Nduwimana, R. N. Musin, A. M. Smith, and X.-Q. Wang, Nano. Lett. 8, 3341 (2008).

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported license. See: http://creativecommons.org/licenses/by/3.0/

Downloaded to IP: 209.172.228.248 On: Sun, 23 Nov 2014 23:07:39