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Growth and field emission property of ZnO nanograsses
Materials Letters 115 (2014) 176–179
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Growth and field emission property of ZnO nanograsses H.M. Dong, Y.H. Yang n, G.W. Yang State Key Laboratory of Optoelectronic Materials and Technologies, Institute of Optoelectronic and Functional Composite Materials, Nanotechnology Research Center, School of Physics & Engineering, Sun Yat-sen University, Guangzhou 510275, Guangdong, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 20 August 2013 Accepted 14 October 2013 Available online 19 October 2013
Well-aligned ZnO nanograsses are fabricated on silicon substrate using thermal chemical vapor transport and condensation (CVTC). The field emission property of ZnO nanograsses array is characterized. The low turn-on electronic field and the high current density are achieved with ZnO nanograsses array as the emitters. It is suggested that the special morphology of ZnO nanograsses play a crucial role for its excellent field emission property, and well aligned ZnO nanograsses can be a promising candidate for an emitter. The growth mechanism of ZnO nanograsses can be explained by the combination of vapor–solid (VS) and vapor–liquid–solid (VLS) processes. The higher ZnO concentration around the silicon substrate and metal catalyst seem to play crucial roles in the formation of ZnO nanograsses. & 2013 Elsevier B.V. All rights reserved.
Keywords: Nanocrystalline materials Triangle-shaped Field emission Crystal growth
1. Introduction One-dimensional zinc oxide (ZnO) nanostructures have attracted great attention because of its particular properties and potential applications in nanodevice fabrication [1]. Meanwhile, ZnO nanostructures are excellent field emission material due to their high mechanical stability, high aspect ratio, negative electron affinity and controllable morphology in various vacuum environments [2–4]. Recently, field-emission properties of various ZnO nanostructures have been reported, such as well aligned ZnO nanowires [2], micro- and nanostructures of ZnO [5], ZnO nanoneedles [6] and tetrapod-like ZnO nanostructures [7]. These works reveal that the morphology and the alignment of nanostructures are the key factors for its field emission property. Therefore, ZnO nanostructures can obtain excellent field emission property by adjusting its morphology. In this paper, ZnO nanograsses have been grown on silicon substrate that the growth of ZnO nanograsses is based on the combination of vapor–solid and vapor– liquid–solid processes. Interestingly, we find that ZnO nanograsses have excellent field emission property, in which the special morphology plays crucial roles.
2. Experimental section The synthesis of ZnO nanograsses was conducted in a horizontal tube furnace by using CVTC. The Au layer about 10 nm in thickness was first deposited on the silicon wafer. In detail, a n
Corresponding author. Tel./fax: þ 86 208 411 5943. E-mail address: [email protected] (Y.H. Yang).
0167-577X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2013.10.046
mixture source of ZnO (50 wt%) and graphite powders (50 wt%) was placed into a small quartz tube and the silicon wafer was put near the mixture source to act as a substrate. The small quartz tube was pulled into a horizontal tube furnace. Then the system was rapidly heated to 1000 1C in 30 min and kept for 30 min under a pressure of 7 104 Pa. A mixed gas of argon gas (280 sccm) and oxygen gas (20 sccm) was the carrier gas. After the growth, the system was cooled down to room temperature. The gray film was observed on the substrate when substrate was moved out. Field emission scanning electron microscope (FESEM) and X-ray diffraction (XRD) were employed to characterize the morphology and structure of prepared samples. Field emission plots were used to characterize the field emission properties of samples. 3. Results and discussion Fig. 1 shows typical FESEM images and XRD patterns of samples. In Fig. 1(a and b), the grass-like nanostructures array is found on the surface of substrate. According to the inset of Fig. 1 (a), these nanograsses are triangle-shaped and have small apex angle (211). The bottom and tip of nanograsses are about 2 μm and 25 nm respectively, which means that the size has changed drastically along its axial direction. Fig. 1(c) shows XRD pattern of our sample. The prepared nanograsses can be indexed to typically hexagonal ZnO with lattice constants a ¼3.2535 Å and c¼5.2056 Å. No silicon oxide peak is visible. It means that the crystalline and dispersion of our sample is good. The low-magnified TEM bright-field image of ZnO nanograsses is shown in Fig. 2(a). Selected area electron diffraction (SAED) image reveals that the growth direction of ZnO nanograsses is along [100] as shown in Fig. 2(b). The corresponding high
H.M. Dong et al. / Materials Letters 115 (2014) 176–179
177
1 um
10 um
(101)
10 um
350
250
(201)
(112)
(103)
100
(110)
(102)
150
(002)
200
(100)
Intensity (cps)
300
50
0 30
35
40
45
50
55
60
65
70
75
80
2theta (deg) Fig. 1. The top and tilt view FESEM image of ZnO nanograsses (a and b) and XRD patter of ZnO nanograsses (c).
resolution-TEM image is shown in Fig. 3(c and d). Combined with SEM images, the growth facets (100) are rarely exposed and some (001) facets can be seen. These result in a powder diffraction pattern (PDF#36-1451), which is consistent with our XRD result (Fig. 1(c)). We measure the field emission properties of our samples using an anode probe technique carried out in an ultrahigh vacuum ( 10 9 Torr) with the distance between the anode and cathode about 300 μm, and the areas of our samples are 5 5 mm2. The measured current densities as a function of the macroscopic electric field are shown in Fig. 3. It can be seen that the turn-on electric field of ZnO nanograsses array is 3.9 V/μm at a current density of 10 uA/cm2. The threshold electronic fields that mean the field value at the emission current density of 1 mA/cm2 are 5.6 V/μm. The reported values of the turn-on and threshold electronic field of ZnO nanoneedles [8], awl-shaped nanorods [9] and Ga-doped nanowires [10] are from 3.4 to 5.2 V/μm and 5.4 to 7.2 V/μm in the literature. As we know, the distribution density of nanostructures will influence its field emission. Compared with the above reports [8–10], our ZnO nanograsses have better field emission property under the same distribution density, which means the morphology of nanograsses plays an important role for its field emission property. In addition, the relevant element doping in nanostructures can enhance the electronics emission in the process of field emission [10,11], in our case, no element was doped in nanograsses. The Fowler–Nordheim plots of ZnO nanograsses are shown in the inset of Fig. 3 and the measured data fit
to linear relationship by lnðI=V 2 Þ ¼ lnðAβ S=Φd Þ BΦ 2
2
6
3=2
2
d=ðβ U VÞ
where A ¼ 1:54 10 ðAV eVÞ; B ¼ 6:83 109 ðeV 3=2 V m 1 Þ, V is the applied voltage between the anode and cathode, β is the field enhancement factor and Φ is the work function of an emitting material. In our case, Φ ¼5.3 eV is the work function of ZnO [2]. Thus β-value of ZnO nanograsses is calculated to reach up to 2011, which means the field emission property is good. Generally, field emission properties of nanostructures depend on their morphology, structure and crystallinity [12,13]. For our ZnO nanograsses, its excellent field emission property can also attribute to the special morphology. The small tip size and high aspect ratio of nanograsses can generate a high local electric field, which will decrease the field emission potential barrier and increase the field emission current. On the other hand, the screening effect between adjacent emitters plays an important role in actual field-emission process. The higher the nanostructures density which means the smaller inter-particle distance, the stronger the degree of the screening effect, and the lower the field enhancement factor β [14,15]. In our case, even the distance between the bottoms of two nanograsses is zero, the distance between their tips is still appreciable. It further proves that the morphology of ZnO nanograsses is benefit for its field emission property. As to the growth of ZnO nanograsses, we can see that the nanoparticles are located on the top of nanograsses in Fig. 1(a). It
178
H.M. Dong et al. / Materials Letters 115 (2014) 176–179
Fig. 2. TEM images and SAED pattern of ZnO nanograsses (a) and (b) and HRTEM image of ZnO nanograss (c and d). -9
1.0
-10
Current density (mA/cm2)
-11
0.8 -12
-13
0.6
-14
0.4
0.0006
0.0008
0.0010
0.0012
0.2
0.0 3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
E (v/um) Fig. 3. Field emission current densities of ZnO nanograsses as a function of macroscopic electronic field; the corresponding Fowler–Nordheim plot is shown in the inset.
means that the growth of nanograsses is VLS process. However, during the growth, the concentration of ZnO molecules is much higher, which will plays a crucial role in the formation of nanograsses [16].
Considering it, we suggest that the growth mechanism of ZnO nanograsses can be explained by the combination of VS and VLS processes as shown in Fig. 4. Firstly, Zn vapor is generated and transported by the carrier gas. Most of Zn vapor will be oxidized. As shown in Fig. 4(a), ZnO molecules deposit on the substrate. Through continuously diffusing and colliding, ZnO clusters would form and can coalesce together with the Au particles, then the nucleation of ZnO takes place and orienting growth of ZnO nuclei occurs. During the growth, ZnO adatoms diffuse to the growth surface along the growth direction. Then adatoms on the growth surface will aggregate to form two-dimensional (2D) crystalline nuclei, and then these 2D crystalline nuclei will coalesce together to form a new surface, which make the crystal grow layer-by-layer. The relative concentration of adatoms on the growth surface controls the growth mode [16]. Moreover, there would be a spontaneously increasing concentration of ZnO adatoms on the growth surface of ZnO nanostructures in the latter part of growth via CVTC [16]. When the relative concentration of reactant atoms is enough large, the mode of the growth surface of ZnO nanostructures naturally starts to transform from ledge-flow to twodimensional nucleation and island growth. And the change in growth mode makes the radial size of ZnO nanograss shrink. On the other hand, a part of Zn vapor will adsorb on Au particles to form Au–Zn alloy droplets. When the Au–Zn alloy reach to the state of supersaturation, Zn atoms will separate out and be oxidized to form ZnO. The precipitation of ZnO can promote the formation of threedimensional crystalline nucleus on the growth surface, which further contributing to the growth of triangle-shaped ZnO nanograss [16]. So, we conclude that the growth mechanism is suggested to the combination of VS and VLS processes.
H.M. Dong et al. / Materials Letters 115 (2014) 176–179
Si substrate Fig. 4. The schematic illustration of ZnO nanograss growth.
4. Conclusion
References
In this paper, we synthesize ZnO nanograsses arrays on the silicon substrates via the thermal chemical vapor transport and condensation method. Its special morphology results in its excellent field emission property. The growth mechanism of ZnO nanograsses is suggested to the combination of VS and VLS processes. These findings provide useful information for applications of ZnO nanostructures in optoelectronic devices.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
Acknowledgments The authors thank the National Natural Science Foundation of China (51002192), Project supported by the Foundation for the Author of Excellent Doctoral Dissertation of Guangdong Province.
Xia Y, Yang P, Sun Y, Wu Y, et al. Adv Mater 2003;15:353. Dong LF, Jiao J, Tuggle DW, et al. Appl Phys Lett 2003;82:1096. Jo SH, Lao JY, Ren ZF, Farre RA, et al. Appl Phys Lett 2004;83:4821. Wang B, Jin X, Ouyang ZB, Xu P. Appl Phys A 2012;108:195. Yang YH, Wang B, Xu NS, Yang GW. Appl Phys Lett 2006;89:043108. Zhu YW, Zhang HZ, Sun XC, et al. Appl Phys Lett 2003;83:144. Li QH, Wan Q, Chen YJ, Wang TH, et al. Appl Phys Lett 2004;85:636. Liu JP, Huang XT, Li YY. J Phys Chem C 2007;111:4990. Wang B, Jin X, Ouyang ZB, Xu P. Appl Phys A 2012;108:195. Chang LW, Yeh JW, Cheng CL, et al. Appl Surf Sci 2011;257:3145. Wang B, Jin X, Ouyang ZB, Xu P. J Nanopart Res 2012;14:1008. Wan Q, Yu K, Wang TH, Lin CL. Appl Phys Lett 2003;83:2253. Banerjee D, Jo SH, Ren ZF. Adv Mater 2004;16:2028. Cao BQ, Teng XM, Heo. SH, et al. J Phys Chem C 2007;111:2470. Zhao Q, Xu J, Xu XY, Wang Z, Yu DP. Appl Phys Lett 2004;85:5331. Yang YH, Wang B, Yang GW. Nanotechnology 2006;17:5556.
179
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Growth and field emission property of ZnO nanograsses H.M. Dong, Y.H. Yang n, G.W. Yang State Key Laboratory of Optoelectronic Materials and Technologies, Institute of Optoelectronic and Functional Composite Materials, Nanotechnology Research Center, School of Physics & Engineering, Sun Yat-sen University, Guangzhou 510275, Guangdong, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 20 August 2013 Accepted 14 October 2013 Available online 19 October 2013
Well-aligned ZnO nanograsses are fabricated on silicon substrate using thermal chemical vapor transport and condensation (CVTC). The field emission property of ZnO nanograsses array is characterized. The low turn-on electronic field and the high current density are achieved with ZnO nanograsses array as the emitters. It is suggested that the special morphology of ZnO nanograsses play a crucial role for its excellent field emission property, and well aligned ZnO nanograsses can be a promising candidate for an emitter. The growth mechanism of ZnO nanograsses can be explained by the combination of vapor–solid (VS) and vapor–liquid–solid (VLS) processes. The higher ZnO concentration around the silicon substrate and metal catalyst seem to play crucial roles in the formation of ZnO nanograsses. & 2013 Elsevier B.V. All rights reserved.
Keywords: Nanocrystalline materials Triangle-shaped Field emission Crystal growth
1. Introduction One-dimensional zinc oxide (ZnO) nanostructures have attracted great attention because of its particular properties and potential applications in nanodevice fabrication [1]. Meanwhile, ZnO nanostructures are excellent field emission material due to their high mechanical stability, high aspect ratio, negative electron affinity and controllable morphology in various vacuum environments [2–4]. Recently, field-emission properties of various ZnO nanostructures have been reported, such as well aligned ZnO nanowires [2], micro- and nanostructures of ZnO [5], ZnO nanoneedles [6] and tetrapod-like ZnO nanostructures [7]. These works reveal that the morphology and the alignment of nanostructures are the key factors for its field emission property. Therefore, ZnO nanostructures can obtain excellent field emission property by adjusting its morphology. In this paper, ZnO nanograsses have been grown on silicon substrate that the growth of ZnO nanograsses is based on the combination of vapor–solid and vapor– liquid–solid processes. Interestingly, we find that ZnO nanograsses have excellent field emission property, in which the special morphology plays crucial roles.
2. Experimental section The synthesis of ZnO nanograsses was conducted in a horizontal tube furnace by using CVTC. The Au layer about 10 nm in thickness was first deposited on the silicon wafer. In detail, a n
Corresponding author. Tel./fax: þ 86 208 411 5943. E-mail address: [email protected] (Y.H. Yang).
0167-577X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2013.10.046
mixture source of ZnO (50 wt%) and graphite powders (50 wt%) was placed into a small quartz tube and the silicon wafer was put near the mixture source to act as a substrate. The small quartz tube was pulled into a horizontal tube furnace. Then the system was rapidly heated to 1000 1C in 30 min and kept for 30 min under a pressure of 7 104 Pa. A mixed gas of argon gas (280 sccm) and oxygen gas (20 sccm) was the carrier gas. After the growth, the system was cooled down to room temperature. The gray film was observed on the substrate when substrate was moved out. Field emission scanning electron microscope (FESEM) and X-ray diffraction (XRD) were employed to characterize the morphology and structure of prepared samples. Field emission plots were used to characterize the field emission properties of samples. 3. Results and discussion Fig. 1 shows typical FESEM images and XRD patterns of samples. In Fig. 1(a and b), the grass-like nanostructures array is found on the surface of substrate. According to the inset of Fig. 1 (a), these nanograsses are triangle-shaped and have small apex angle (211). The bottom and tip of nanograsses are about 2 μm and 25 nm respectively, which means that the size has changed drastically along its axial direction. Fig. 1(c) shows XRD pattern of our sample. The prepared nanograsses can be indexed to typically hexagonal ZnO with lattice constants a ¼3.2535 Å and c¼5.2056 Å. No silicon oxide peak is visible. It means that the crystalline and dispersion of our sample is good. The low-magnified TEM bright-field image of ZnO nanograsses is shown in Fig. 2(a). Selected area electron diffraction (SAED) image reveals that the growth direction of ZnO nanograsses is along [100] as shown in Fig. 2(b). The corresponding high
H.M. Dong et al. / Materials Letters 115 (2014) 176–179
177
1 um
10 um
(101)
10 um
350
250
(201)
(112)
(103)
100
(110)
(102)
150
(002)
200
(100)
Intensity (cps)
300
50
0 30
35
40
45
50
55
60
65
70
75
80
2theta (deg) Fig. 1. The top and tilt view FESEM image of ZnO nanograsses (a and b) and XRD patter of ZnO nanograsses (c).
resolution-TEM image is shown in Fig. 3(c and d). Combined with SEM images, the growth facets (100) are rarely exposed and some (001) facets can be seen. These result in a powder diffraction pattern (PDF#36-1451), which is consistent with our XRD result (Fig. 1(c)). We measure the field emission properties of our samples using an anode probe technique carried out in an ultrahigh vacuum ( 10 9 Torr) with the distance between the anode and cathode about 300 μm, and the areas of our samples are 5 5 mm2. The measured current densities as a function of the macroscopic electric field are shown in Fig. 3. It can be seen that the turn-on electric field of ZnO nanograsses array is 3.9 V/μm at a current density of 10 uA/cm2. The threshold electronic fields that mean the field value at the emission current density of 1 mA/cm2 are 5.6 V/μm. The reported values of the turn-on and threshold electronic field of ZnO nanoneedles [8], awl-shaped nanorods [9] and Ga-doped nanowires [10] are from 3.4 to 5.2 V/μm and 5.4 to 7.2 V/μm in the literature. As we know, the distribution density of nanostructures will influence its field emission. Compared with the above reports [8–10], our ZnO nanograsses have better field emission property under the same distribution density, which means the morphology of nanograsses plays an important role for its field emission property. In addition, the relevant element doping in nanostructures can enhance the electronics emission in the process of field emission [10,11], in our case, no element was doped in nanograsses. The Fowler–Nordheim plots of ZnO nanograsses are shown in the inset of Fig. 3 and the measured data fit
to linear relationship by lnðI=V 2 Þ ¼ lnðAβ S=Φd Þ BΦ 2
2
6
3=2
2
d=ðβ U VÞ
where A ¼ 1:54 10 ðAV eVÞ; B ¼ 6:83 109 ðeV 3=2 V m 1 Þ, V is the applied voltage between the anode and cathode, β is the field enhancement factor and Φ is the work function of an emitting material. In our case, Φ ¼5.3 eV is the work function of ZnO [2]. Thus β-value of ZnO nanograsses is calculated to reach up to 2011, which means the field emission property is good. Generally, field emission properties of nanostructures depend on their morphology, structure and crystallinity [12,13]. For our ZnO nanograsses, its excellent field emission property can also attribute to the special morphology. The small tip size and high aspect ratio of nanograsses can generate a high local electric field, which will decrease the field emission potential barrier and increase the field emission current. On the other hand, the screening effect between adjacent emitters plays an important role in actual field-emission process. The higher the nanostructures density which means the smaller inter-particle distance, the stronger the degree of the screening effect, and the lower the field enhancement factor β [14,15]. In our case, even the distance between the bottoms of two nanograsses is zero, the distance between their tips is still appreciable. It further proves that the morphology of ZnO nanograsses is benefit for its field emission property. As to the growth of ZnO nanograsses, we can see that the nanoparticles are located on the top of nanograsses in Fig. 1(a). It
178
H.M. Dong et al. / Materials Letters 115 (2014) 176–179
Fig. 2. TEM images and SAED pattern of ZnO nanograsses (a) and (b) and HRTEM image of ZnO nanograss (c and d). -9
1.0
-10
Current density (mA/cm2)
-11
0.8 -12
-13
0.6
-14
0.4
0.0006
0.0008
0.0010
0.0012
0.2
0.0 3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
E (v/um) Fig. 3. Field emission current densities of ZnO nanograsses as a function of macroscopic electronic field; the corresponding Fowler–Nordheim plot is shown in the inset.
means that the growth of nanograsses is VLS process. However, during the growth, the concentration of ZnO molecules is much higher, which will plays a crucial role in the formation of nanograsses [16].
Considering it, we suggest that the growth mechanism of ZnO nanograsses can be explained by the combination of VS and VLS processes as shown in Fig. 4. Firstly, Zn vapor is generated and transported by the carrier gas. Most of Zn vapor will be oxidized. As shown in Fig. 4(a), ZnO molecules deposit on the substrate. Through continuously diffusing and colliding, ZnO clusters would form and can coalesce together with the Au particles, then the nucleation of ZnO takes place and orienting growth of ZnO nuclei occurs. During the growth, ZnO adatoms diffuse to the growth surface along the growth direction. Then adatoms on the growth surface will aggregate to form two-dimensional (2D) crystalline nuclei, and then these 2D crystalline nuclei will coalesce together to form a new surface, which make the crystal grow layer-by-layer. The relative concentration of adatoms on the growth surface controls the growth mode [16]. Moreover, there would be a spontaneously increasing concentration of ZnO adatoms on the growth surface of ZnO nanostructures in the latter part of growth via CVTC [16]. When the relative concentration of reactant atoms is enough large, the mode of the growth surface of ZnO nanostructures naturally starts to transform from ledge-flow to twodimensional nucleation and island growth. And the change in growth mode makes the radial size of ZnO nanograss shrink. On the other hand, a part of Zn vapor will adsorb on Au particles to form Au–Zn alloy droplets. When the Au–Zn alloy reach to the state of supersaturation, Zn atoms will separate out and be oxidized to form ZnO. The precipitation of ZnO can promote the formation of threedimensional crystalline nucleus on the growth surface, which further contributing to the growth of triangle-shaped ZnO nanograss [16]. So, we conclude that the growth mechanism is suggested to the combination of VS and VLS processes.
H.M. Dong et al. / Materials Letters 115 (2014) 176–179
Si substrate Fig. 4. The schematic illustration of ZnO nanograss growth.
4. Conclusion
References
In this paper, we synthesize ZnO nanograsses arrays on the silicon substrates via the thermal chemical vapor transport and condensation method. Its special morphology results in its excellent field emission property. The growth mechanism of ZnO nanograsses is suggested to the combination of VS and VLS processes. These findings provide useful information for applications of ZnO nanostructures in optoelectronic devices.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
Acknowledgments The authors thank the National Natural Science Foundation of China (51002192), Project supported by the Foundation for the Author of Excellent Doctoral Dissertation of Guangdong Province.
Xia Y, Yang P, Sun Y, Wu Y, et al. Adv Mater 2003;15:353. Dong LF, Jiao J, Tuggle DW, et al. Appl Phys Lett 2003;82:1096. Jo SH, Lao JY, Ren ZF, Farre RA, et al. Appl Phys Lett 2004;83:4821. Wang B, Jin X, Ouyang ZB, Xu P. Appl Phys A 2012;108:195. Yang YH, Wang B, Xu NS, Yang GW. Appl Phys Lett 2006;89:043108. Zhu YW, Zhang HZ, Sun XC, et al. Appl Phys Lett 2003;83:144. Li QH, Wan Q, Chen YJ, Wang TH, et al. Appl Phys Lett 2004;85:636. Liu JP, Huang XT, Li YY. J Phys Chem C 2007;111:4990. Wang B, Jin X, Ouyang ZB, Xu P. Appl Phys A 2012;108:195. Chang LW, Yeh JW, Cheng CL, et al. Appl Surf Sci 2011;257:3145. Wang B, Jin X, Ouyang ZB, Xu P. J Nanopart Res 2012;14:1008. Wan Q, Yu K, Wang TH, Lin CL. Appl Phys Lett 2003;83:2253. Banerjee D, Jo SH, Ren ZF. Adv Mater 2004;16:2028. Cao BQ, Teng XM, Heo. SH, et al. J Phys Chem C 2007;111:2470. Zhao Q, Xu J, Xu XY, Wang Z, Yu DP. Appl Phys Lett 2004;85:5331. Yang YH, Wang B, Yang GW. Nanotechnology 2006;17:5556.
179