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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 14426–14433
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Room temperature electrically pumped ultraviolet random lasing from ZnO nanorod arrays on Si

Xiangyang Ma, Jingwei Pan, Peiliang Chen, Dongsheng Li, Hui Zhang, Yang Yang, and Deren Yang  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 14426-14433 (2009)
http://dx.doi.org/10.1364/OE.17.014426


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Abstract

We report the electrically pumped ultraviolet random lasing from ZnO nanorod arrays on Si. Metal-insulator-semiconductor structures in a form of Au/SiO2/ZnO-nanorod-array were fabricated on Si. Such devices exhibit random lasing when the Au electrode is applied with a sufficiently high positive voltage. In this context, in the region adjacent to SiO2/ZnO-nanorod-array interface, stimulated emission from ZnO occurs due to population inversion and, moreover, light is scattered by the nanorods and SiO2 films. Therefore, random lasing proceeds due to optical gain achieved by the stimulated emission and multiple scattering.

© 2009 OSA

1. Introduction

Previously, we have reported the electrically pumped random lasing from c-axis oriented ZnO films taking advantage of metal-insulator-semiconductor (MIS) structures [13

13. X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91(25), 251109 (2007). [CrossRef]

,14

14. P. Chen, X. Ma, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ultraviolet random lasing from ZnO-based metal-insulator-semiconductor devices: dependence on carrier transport,” Opt. Express 17(6), 4712–4717 (2009). [CrossRef] [PubMed]

]. For the ZnO film, the grains are closely packed in the plane of film. In this case, optical scattering that is critical for random lasing proceeds via the grain boundaries. It is generally believed that the optical scattering is strong in a space with variation of refractive index (nr) [15

15. S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004). [CrossRef]

]. Evidently, it is quite difficult to substantially enhance the spatial variation of nr within ZnO film. While, for ZnO nanorod array, the spatial variation of nr can be flexibly modified because there are interspaces among the nanorods, which offer the possibility of filling foreign materials with nr different from that of ZnO. Therefore, ZnO nanorod array predominates over ZnO film for the enhancement of optical scattering. Nevertheless, the electrically pumped random lasing from ZnO nanorod arrays has not been reported as yet. Generally, current injection via a p-n junction is preferred for the electrical pumping of diode lasers. Unfortunately, it is quite difficult to fabricate ZnO-nanorod-based p-n junctions due to the difficulty in p-type doping of the ZnO nanorods. In this paper, we have electrically driven the ZnO nanorod arrays to generate random lasing by means of the Au/SiO2/ZnO-nanorod-array MIS structures. In our strategy, both the ZnO nanorod arrays and SiO2 film are prepared by simple chemical routes. Moreover, the difficulty in p-type doping of ZnO nanorods is avoided. To the best of our knowledge, the electrically pumped random lasing from ZnO nanorod arrays is firstly demonstrated. More importantly, the ZnO naonorod arrays allow accommodation of other optically functional materials. This virtue might be used to develop diverse optoelectronic devices based on the proof-of-concept random lasers presented herein.

2. Experimental details

Figure 1 shows the schematic diagram of a MIS device based on the ZnO nanorod array on Si substrate. In our experiment, the devices were fabricated through the procedures as described below. Firstly, ~50 nm thick ZnO thin films, which acted as the seed layers for the subsequent growth of ZnO nanorod arrays, were deposited on 1.5 × 1.5 cm2 (100) heavily arsenic-doped Si substrates (n-type, with an electron concentration of ~5 × 1019cm-3) by reactive DC sputtering. Secondly, the above-mentioned Si substrates coated with the ZnO films were vertically hung in a mixed solution heated to 90°C. The mixed solution was formed by adding 890 mg of Zn(NO3)2 and 420 mg of diethylenetriamine into 100 mL of deionized water. In this way, vertically aligned ZnO nanorod arrays were grown on the silicon substrates. After a growth time of 2 h, the silicon substrates covered with ZnO nanorod arrays were taken out of the solution. Then, they were ultrasonically cleaned in deionized water for 3 min to remove the unwanted ZnO particles adhering on the ZnO nanorod arrays. In order to improve the crystallinity, the as-deposited ZnO nanorod arrays on the silicon substrates were annealed at 700°C for 2 h. Thirdly, ~90 nm thick SiO2 films were deposited onto the ZnO nanorod arrays by a sol-gel process consisting of the following steps: i) spin-coating of a precursor sol consisting of TEOS: EtOH: H2O = 1: 10: 4 (molar ratio) in which a properly small amount of HNO3 was added as the catalyzer, ii) soft-bake at 60°C for 20 min to remove the solvents in the gel, iii) annealing at 650°C for 2 h under O2 ambient. Finally, ~20 nm thick Au film on the SiO2 film and ~100 nm thick Au film on the backside of silicon substrate were successively sputtered as the electrodes. Either electrode was patterned into a circle with a diameter of ~10 mm.

The EL spectra for the devices under different DC voltages were recorded at RT using an Acton spectraPro 2500i spectrometer with a lowest spectrum resolution of 0.5 Å and an accuracy of ± 2 Å. For the acquisition of spectrum, the scanning step size was 1 Å. Moreover, the output power was measured using a Newport 1931-C power meter with an 818-UV/DB detector (~1cm in diameter). For the measurement, the devices were brought face to face with the detector. The devices were ~2 cm apart from the detector. For such a measurement configuration, it is roughly calculated that only ~2% of the output power of a device is detected by the above-mentioned power meter.

Fig. 1. Schematic diagram of the metal (Au)-insulator (SiO2)-semiconductor (ZnO nanorod array) structure on Si substrate.

3. Results and discussion

Fig. 2. (a). Plan-view and (b) cross-sectional view images of the ZnO nanorod array annealed at 700°C for 2 h. (c) PL spectra of ZnO nanorod array before and after 700°C/2 h annealing.
Fig. 3. (a). Current-voltage characteristic of the MIS device based on ZnO nanorod array. (b). EL spectra of the device under different forward bias voltages. (c). Detected output power as a function of the injection current.

Figure 3a shows the current-voltage (I-V) characteristic of a typical device. Because the sol-gel derived SiO2 film is much poorer in insulation performance with respect to the thermal-oxidation-grown SiO2 film, there is a remarkable current through the device at a sufficiently high forward bias voltage. This is critical for the EL from the device. Herein, forward/reverse bias means that the gate electrode of Au is connected to positive/negative voltage. As can be seen, the device exhibits a rectifying behavior to a great extent. It is found that the MIS devices based on ZnO nanorod arrays are electroluminescent only under forward bias.

Figure 3b shows the evolution of the EL spectra for a device with the increase of forward bias voltage. At 4 V, the EL spectrum is greatly spoiled by the noises, illustrating as a single broad spontaneous emission peak centered at around 383 nm, which is ascribed to the NBE UV emission from ZnO. As the voltage is a little bit increased to 4.5 V, a few of discrete narrow peaks emerge in the spectrum. The linewidth of these peaks is less than 2 Å. When the voltage is further increased to 5 V and above, more sharp peaks appear in the spectra. Moreover, the EL intensity is significantly increased. The detected output power as a function of injection current is shown in Fig. 3c. Above a threshold current, as shown by a solid line plotted to guide the eyes, the output power increases linearly with the injection current. Such a linear dependence is due to the gain saturation that forms an intrinsic aspect of an amplifying system above threshold [17

17. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]

]. The narrow linewidth and the rapid increase of emission intensity, as shown in Figs. 3b and 3c, indicate the occurrence of lasing from the device. Note Fig. 3b that the spacing between the adjacent sharp peaks is not uniform. Therefore, we believe that the laser spikes in the EL spectra are ascribed to the random lasing from ZnO nanorod array. Evidently, the multiple sharp peaks in the spectra between 360 and 400 nm, as shown in Fig. 3b, represent different lasing modes.

It should be stated that the device exhibits no essential visible EL in the visible region. Figure 4 shows the EL spectrum in the wavelength range of 360–800 nm for the device applied with a forward bias of 8 V. As can be seen, in the visible wavelength region of 450–800 nm there is no discernable peak except the band centered at ~760 nm, which belongs to the second harmonics of the UV emission. This is also the case for the device applied with other forward bias voltages. The reason for no substantial visible EL from the device is elucidated below.

Fig. 4. EL spectrum in the wavelength range of 360–800 nm for the MIS device applied with a forward bias of 8 V.

Figure 5 shows a series of EL spectra taken at three successive measurements for the device applied with a forward bias of 8 V. Herein, it took ~60 s for each cycle of measurement. In the three spectra, the number and height of the sharp peaks are quite different. Moreover, the wavelengths corresponding to the sharp peaks change randomly. Such features of the emission spectra illustrate the intrinsic aspects of random lasing. It is reasonably believed that the electrically pumped random lasing from the ZnO nanorod array exhibits a different spectrum every moment. Definitely, in the random laser the light is multiply scattered and amplified by stimulated emission. For certain modes of the light, they achieve optical gain larger than the losses. As a consequence, the narrow emission spikes emerge in the emitted spectrum in the case of specific measurement configuration [17

17. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]

]. In the device, the light emitted every moment is subsequently scattered with random walks. Therefore, the modes which can achieve optical gain larger than the losses are varying every moment in terms of wavelength and intensity. The scenario as described above can be believed to be vividly embodied in Fig. 5. Actually, in the case of optically pumped random laser action, it has been found that the narrow emission spikes in the emitted spectrum can change frequency randomly from one excitation pulse to another. This chaotic behavior is ascribed to the fact that the random lasing starts from spontaneous emission which is different at each shot [18

18. S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007). [CrossRef]

].

Fig. 5. Series of EL spectra taken at successive measurement cycles.

Understandably, both electron and hole concentrations increase with forward bias. Above a critical forward bias, the electron concentration in the band-downward region adjacent to the ZnO-nanorod/SiO2 interface is considerably high so that the quasi Fermi level of electron (EFn) enters into the conduction band. On the other hand, due to the considerably small hole mobility in ZnO, most of the injected holes in the ZnO nanorod are also populated in the band-downward region nearby the ZnO-nanorod/SiO2 interface, as shown in Fig. 6a. Under a sufficiently high forward bias, the hole concentration in the band-downward region is high enough to enable the quasi Fermi level of hole (EFp) to be close to the edge of valence band (case 1) and even to enter into the valence band (case 2). The above-mentioned scenario can be illustrated in terms of density of states diagram for the band-downward region, as schematically shown in Fig. 6b. Accordingly, with a high carrier injection level under forward bias larger than a critical voltage, the condition for population inversion in ZnO, that is, EFn - EFp > Eg (band gap), is satisfied. Consequently, the stimulated emission can occur in the device. Then, the spontaneous emission can be amplified.

Fig. 6. (a) Schematic band diagram of a sufficiently forward-biased MIS structure of Au/SiO2/ZnO-nanorod on Si. (b) The density of states and energy distribution of electrons and holes in the conduction and valence bands respectively in the band-downward region adjacent to SiO2/ZnO-nanorod interface under forward bias such that EFn - EFp > Eg. (c) Schematic illustration of quasi-2D random walks in the region close to the nanorods/SiO2 interface.

It should be stated that the stimulated emission only occurs in the band-downward region because the carrier concentrations are too low elsewhere. Therefore, the light emission in the device is primarily localized in a quasi two-dimensional (2D) region close to the ZnO-nanorod-array/SiO2 interface. Moreover, the ZnO nanorod array acts as a 2D scattering system, as light is scattered by the nanorods in the plane perpendicular to the rods [19

19. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. Math. Gen. 38(49), 10497–10535 (2005). [CrossRef]

]. In our device, the ZnO nanorods and the SiO2 films penetrating into the interspaces within the ZnO nonorod array, form a disorder network in the plane perpendicular to the nanorods. There is a refractive index mismatch between ZnO and SiO2, which facilitates the light scattering. Figure 6c shows a quasi-2D type of light transport in the region close to the nanorods/SiO2 interface, where multiple light scattering takes place. Although the picture of closed-loop random cavity can be well used to account for the random lasing [20

20. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]

], it is argued that an unrealistically high gain will be required to achieve the lasing threshold condition in such a loop since most of the energy is scattered out of the loop in each scattering act [21

21. V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89(1), 016802 (2002). [CrossRef] [PubMed]

]. Nevertheless, it has been theoretically derived that random resonators that correspond to certain arrangement of scatterers can form in a quasi 2D system with the random variations of nr [21

21. V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89(1), 016802 (2002). [CrossRef] [PubMed]

]. According to this viewpoint, we believe that the random resonators should form in our device where the random variations of nr are induced by the random distribution of the ZnO nanorods and SiO2 films. In this context, once the optical gain is larger than the losses when the device is applied with a sufficiently high forward bias, the device will lase thus leading to spectrally narrow emission.

Moreover, according to the mechanism presented in Ref. 22

22. S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903 (2004). [CrossRef] [PubMed]

, we can alternatively interpret the electrically pumped random lasing from our devices. As mentioned above, the region adjacent to the ZnO-nanorod-array/SiO2 interface becomes a quasi 2D amplifying disordered system as the device is sufficiently forward-biased. Each individual sharp peak in Fig. 2b corresponds to a single spontaneous emission event that fortunately propagates with a very long light path due to the multiple scattering and picks up a gain larger than the losses through the stimulated emission. In other words, a number of spontaneously emitted photons experience extraordinarily multiple scattering to achieve gain that is larger than the losses, leading to laser spikes in the emitted spectrum.

4. Conclusion

In summary, we have demonstrated the electrically pumped random lasing from the ZnO nanorod arrays which acts as the component of semiconductor in the MIS devices in which Au and SiO2 are the metal gate and insulator layer, respectively. When the MIS devices are applied with a sufficiently high forward bias, in the region adjacent to the ZnO nanorods/SiO2 interface, the stimulated emission that provides optical gain occurs. In the mean time, the quasi 2D type of random light transport proceeds via multiple scattering facilitated by the random variations of nr, which are induced by the randomly distributed ZnO nanorods and SiO2 films. Therefore, the devices can be electrically pumped to achieve optical gain through stimulated emission together with multiple scattering. Above a threshold voltage/current, the devices exhibit random laser actions featuring a series of narrow spikes in the emitted spectra.

Acknowledgements

We thank the financial supports from Natural Science Foundation of China (No. 60776045), “973 Program” (No.2007CB613403), and Changjiang Scholars and Innovation Teams in Universities.

References and links

1.

Ü. Özgür, Y. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98(4), 041301 (2005). [CrossRef]

2.

W. Wegscheider, L. N. Pfeiffer, M. M. Dignam, A. Pinczuk, K. W. West, S. L. McCall, and R. Hull, “Lasing from excitons in quantum wires,” Phys. Rev. Lett. 71(24), 4071–4074 (1993). [CrossRef] [PubMed]

3.

Z. K. Tang, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Self-assembled ZnO nano-crystals and exciton lasing at room temperature,” J. Cryst. Growth 287(1), 169–179 (2006). [CrossRef]

4.

M. H. Huang, S. Mao, H. Feick, H. Q. Yan, Y. Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science 292(5523), 1897–1899 (2001). [CrossRef] [PubMed]

5.

J. C. Johnson, K. P. Knutsen, H. Q. Yan, M. Law, Y. F. Zhang, P. D. Yang, and R. J. Saykally, “Ultrafast carrier dynamics in single ZnO naonowire and nanoribbon lasers,” Nano Lett. 4(2), 197–204 (2004). [CrossRef]

6.

S. F. Yu, S. P. Lau, W. I. Park, and G.-C. Yi, “Random laser action in ZnO nanorod arrays embedded in ZnO epilayers,” Appl. Phys. Lett. 84(17), 3241–3243 (2004). [CrossRef]

7.

S. P. Lau, H. Y. Yang, S. F. Yu, H. D. Li, M. Tanemura, T. Okita, H. Hatano, and H. H. Hng, “Laser action in ZnO nanoneedles selectively grown on silicon and plastic substrates,” Appl. Phys. Lett. 87(1), 013104 (2005). [CrossRef]

8.

S. P. Lau, H. Y. Yang, S. F. Yu, C. Yuen, E. S. P. Leong, H. D. Li, and H. H. Hng, “Flexible ultraviolet random lasers based on nanoparticles,” Small 1(10), 956–959 (2005).

9.

B. S. Zou, R. B. Liu, F. F. Wang, A. L. Pan, L. Cao, and Z. L. Wang, “Lasing mechanism of ZnO nanowires/nanobelts at room temperature,” J. Phys. Chem. B 110(26), 12865–12873 (2006). [CrossRef] [PubMed]

10.

J. Z. Liu, S. Lee, Y. H. Ahn, J. Y. Park, K. H. Koh, and K. H. Park, “Identification of dispersion-dependent hexagonal cavity modes of an individual ZnO nanonail,” Appl. Phys. Lett. 92(26), 263102 (2008). [CrossRef]

11.

C. Czekalla, C. Sturm, R. Schmidt-Grund, B. Q. Cao, M. Lorenz, and M. Grundmann, “Whispering gallery mode lasing in Zinc oxide microwires,” Appl. Phys. Lett. 92(24), 241102 (2008). [CrossRef]

12.

D. Wang, H. W. Seo, C.-C. Tin, M. J. Bozack, J. R. Willams, M. Park, and Y. Tzeng, “Lasing in whispering gallery mode in ZnO nanonails,” J. Appl. Phys. 99(9), 093112 (2006). [CrossRef]

13.

X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91(25), 251109 (2007). [CrossRef]

14.

P. Chen, X. Ma, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ultraviolet random lasing from ZnO-based metal-insulator-semiconductor devices: dependence on carrier transport,” Opt. Express 17(6), 4712–4717 (2009). [CrossRef] [PubMed]

15.

S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004). [CrossRef]

16.

A. B. Djurisic and Y. H. Leung, “Optical properties of ZnO nanostructures,” Small 2(8–9), 944–961 (2006).

17.

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]

18.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007). [CrossRef]

19.

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. Math. Gen. 38(49), 10497–10535 (2005). [CrossRef]

20.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]

21.

V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89(1), 016802 (2002). [CrossRef] [PubMed]

22.

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903 (2004). [CrossRef] [PubMed]

OCIS Codes
(140.3610) Lasers and laser optics : Lasers, ultraviolet
(290.5890) Scattering : Scattering, stimulated
(250.5960) Optoelectronics : Semiconductor lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 18, 2009
Revised Manuscript: July 11, 2009
Manuscript Accepted: July 18, 2009
Published: July 31, 2009

Citation
Xiangyang Ma, Jingwei Pan, Peiliang Chen, Dongsheng Li, Hui Zhang, Yang Yang, and Deren Yang, "Room temperature electrically pumped ultraviolet random lasing from ZnO nanorod arrays on Si," Opt. Express 17, 14426-14433 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-14426


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References

  1. Ü. Özgür, Y. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98(4), 041301 (2005). [CrossRef]
  2. W. Wegscheider, L. N. Pfeiffer, M. M. Dignam, A. Pinczuk, K. W. West, S. L. McCall, and R. Hull, “Lasing from excitons in quantum wires,” Phys. Rev. Lett. 71(24), 4071–4074 (1993). [CrossRef] [PubMed]
  3. Z. K. Tang, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Self-assembled ZnO nano-crystals and exciton lasing at room temperature,” J. Cryst. Growth 287(1), 169–179 (2006). [CrossRef]
  4. M. H. Huang, S. Mao, H. Feick, H. Q. Yan, Y. Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science 292(5523), 1897–1899 (2001). [CrossRef] [PubMed]
  5. J. C. Johnson, K. P. Knutsen, H. Q. Yan, M. Law, Y. F. Zhang, P. D. Yang, and R. J. Saykally, “Ultrafast carrier dynamics in single ZnO naonowire and nanoribbon lasers,” Nano Lett. 4(2), 197–204 (2004). [CrossRef]
  6. S. F. Yu, S. P. Lau, W. I. Park, and G.-C. Yi, “Random laser action in ZnO nanorod arrays embedded in ZnO epilayers,” Appl. Phys. Lett. 84(17), 3241–3243 (2004). [CrossRef]
  7. S. P. Lau, H. Y. Yang, S. F. Yu, H. D. Li, M. Tanemura, T. Okita, H. Hatano, and H. H. Hng, “Laser action in ZnO nanoneedles selectively grown on silicon and plastic substrates,” Appl. Phys. Lett. 87(1), 013104 (2005). [CrossRef]
  8. S. P. Lau, H. Y. Yang, S. F. Yu, C. Yuen, E. S. P. Leong, H. D. Li, and H. H. Hng, “Flexible ultraviolet random lasers based on nanoparticles,” Small 1(10), 956–959 (2005).
  9. B. S. Zou, R. B. Liu, F. F. Wang, A. L. Pan, L. Cao, and Z. L. Wang, “Lasing mechanism of ZnO nanowires/nanobelts at room temperature,” J. Phys. Chem. B 110(26), 12865–12873 (2006). [CrossRef] [PubMed]
  10. J. Z. Liu, S. Lee, Y. H. Ahn, J. Y. Park, K. H. Koh, and K. H. Park, “Identification of dispersion-dependent hexagonal cavity modes of an individual ZnO nanonail,” Appl. Phys. Lett. 92(26), 263102 (2008). [CrossRef]
  11. C. Czekalla, C. Sturm, R. Schmidt-Grund, B. Q. Cao, M. Lorenz, and M. Grundmann, “Whispering gallery mode lasing in Zinc oxide microwires,” Appl. Phys. Lett. 92(24), 241102 (2008). [CrossRef]
  12. D. Wang, H. W. Seo, C.-C. Tin, M. J. Bozack, J. R. Willams, M. Park, and Y. Tzeng, “Lasing in whispering gallery mode in ZnO nanonails,” J. Appl. Phys. 99(9), 093112 (2006). [CrossRef]
  13. X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91(25), 251109 (2007). [CrossRef]
  14. P. Chen, X. Ma, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ultraviolet random lasing from ZnO-based metal-insulator-semiconductor devices: dependence on carrier transport,” Opt. Express 17(6), 4712–4717 (2009). [CrossRef] [PubMed]
  15. S. Gottardo, S. Cavalieri, O. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93(26), 263901 (2004). [CrossRef]
  16. A. B. Djurisić and Y. H. Leung, “Optical properties of ZnO nanostructures,” Small 2(8-9), 944–961 (2006).
  17. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]
  18. S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007). [CrossRef]
  19. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. Math. Gen. 38(49), 10497–10535 (2005). [CrossRef]
  20. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]
  21. V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89(1), 016802 (2002). [CrossRef] [PubMed]
  22. S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903 (2004). [CrossRef] [PubMed]

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