APPLIED PHYSICS LETTERS
VOLUME 79, NUMBER 22
26 NOVEMBER 2001
Optical characterization of wurtzite gallium nitride nanowires M. W. Leea) and H. Z. Twu Department of Physics, National Chung-Hsing University, Taichung, 402, Taiwan, Republic of China
C.-C. Chen and C.-H. Chen Department of Chemistry, National Taiwan Normal University, Taipei, 116, Taiwan, Republic of China
共Received 29 May 2001; accepted for publication 29 August 2001兲 The optical properties of the gallium nitride 共GaN兲 nanowires are examined by the transmission method in the ultraviolet-visible range 共1–5 eV兲 and by the reflection method in the infrared range 共500– 4000 cm⫺1兲. The absorption edge of the GaN nanowires is blueshifted by 0.2 eV from the bulk edge. The temperature dependence of the energy gap is expressed by, E g (T)⫽3.724⫺9.97 ⫻10⫺4 /(861⫹T) eV. The plasma frequency and the free-carrier density of the GaN nanowires, deduced from the infrared reflectance minima, are estimated to be p ⫽1100⫾120 cm⫺1 and n f ⫽3.73⫻1017 cm⫺3, respectively. Obtaining the free-carrier density from the infrared reflectance spectra is especially useful in research on nanostructured semiconductors. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1416476兴
Gallium nitride 共GaN兲 is one of the most promising wide-band-gap semiconductors for such potential applications as blue light-emitting diodes 共LED兲 and laser diodes.1,2 GaN-based LEDs have exhibited superior lifetimes and emitted power than have conventional light sources.3 Recently, several research groups have successfully synthesized GaN nanowires using various techniques.4 – 6 These onedimensional nanostructures are expected to exhibit electronic and optical properties that strongly depend on size and geometry. In addition, the surface effect becomes important in thinner nanowires. Surface passivated nanostructured semiconductors exhibit enhanced luminescent efficiency.7 However, the optical properties of one-dimensional GaN have been little explored until now. This letter examines the optical properties of GaN nanowires synthesized by the thermal reaction of gallium and ammonium over catalysts. The optical parameters of the GaN nanowires such as the absorption edge, optical phonon frequencies, plasma frequency, and free-carrier density are determined from the optical results. The infrared reflectance response is modeled by a dielectric function including a phonon term and a Drude term. Analysis results indicate that the infrared response is strongly affected by the free carriers. GaN nanowires were grown from the reaction of Ga and NH3 in the presence of metal catalysts in a tube furnace. Details of the procedure for sample preparation can be found elsewhere.8,9 High-purity and -quality GaN nanowires were obtained by optimizing the growth conditions as follows: heating rate—30 °C–100 °C/min, reaction temperature— 800 °C–1050 °C, reaction time 3– 48 h, and NH3 gas flow rate—18 sccm. Figure 1 displays a typical scanning electron microscope image of an as-grown nanowire sample on a silicon substrate. The materials observed on the substrate were almost all wire like. The synthesized nanowires have lengths up to several micrometers and diameters ranging from 10 to 50 nm. Nanowires with diameters less than 10 nm were also
observed. Structural characterization using x-ray powder diffraction and high-resolution transmission electron microscope confirmed that the wire-like materials were indeed GaN crystals with predominantly wurtzite phase. Figure 2 displays the infrared reflection spectrum of the GaN nanowires over the frequency range 250–2000 cm⫺1. The spectrum was obtained by taking the ratio of the reflection spectrum of the GaN nanowires to that of a gold reference mirror 共an almost perfect reflector in the infrared兲. Three noteworthy features are associated with the spectrum. First, a high reflectance region appears in the range between 500 and 750 cm⫺1. Second, the baseline in the low frequency region ( ⬍1250 cm⫺1) increases with decreasing frequency. Third, two reflection minima, labeled ⫹ , ⫺ , appear at frequencies 1250 cm⫺1 and 515 cm⫺1, respectively. The high reflectance region corresponds to the reststrahlen band. The second and third features are due to the effects of free carriers. Between the longitudinal optical–phonon frequency L and the transverse optical phonon frequency T , the reflectivity can ideally approach 100%. The optical phonon frequencies can therefore be determined from the upper and lower edges of the reststrahlen region. From Fig. 2, we estimate T ⫽562 cm⫺1 and L ⫽730⫾5 cm⫺1. The upper edge of the reststrahlen region is somewhat smeared out due to the free-carrier effect, making L difficult to determine. These
a兲
Author to whom all correspondence should be addressed; electronic mail:
[email protected]
FIG. 1. Scanning electron microscopy image of GaN nanowires.
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Appl. Phys. Lett., Vol. 79, No. 22, 26 November 2001
by a dielectric function , including contributions from free carriers and optical phonons, ⫽ 共 n⫺ik 兲 ⫽ ⬁ 2
FIG. 2. Reflectance spectrum of GaN nanowires. The dashed curve represents the fitting result by using Eq. 共1兲.
optical–phonon frequencies are close to those of bulk GaN.10 The infrared properties of a semiconductor can be modeled
2 ⫾ ⫽
where 0 is the static dielectric constant. Inserting the experimental data ⫾ into Eq. 共2兲, yielded p ⫽1100⫾120 cm⫺1 and hence n f ⫽3.73⫻1017 cm⫺3. The plasma frequency deduced from ⫹ differs from that deduced from ⫺ by approximately 25%, possibly due to the assumption to neglect the damping term. Two weak reflection dips 共⬃630 and 670 cm⫺1兲 appear in the reststrahlen region; the latter, which is also observed in Raman scattering experiment,12 is probably due to a phonon mode induced by a deep-level defect.13 Since these optical features are extremely weak and difficult to be resolved by our Fourier-transform spectroscopy technique, more future work is needed to clarify the origins of these optical features. Figure 3 presents the transmission spectrum of the GaN nanowires at room temperature over the spectral range 1– 4 eV. The spectrum was obtained by taking the ratio of the
冊
共1兲
where n is the refractive index; k is the extinction coefficient; p ⫽(4 n f e 2 /m * ⬁ ) 1/2 is the plasma frequency due to free carriers with density n f , effective mass m * , damping constant ␥, and ⌫ is the damping constant of phonons. The best fit, shown as a dashed line in Fig. 2, reasonably reproduces the experimental spectrum. The fitting parameters are, ␥ ⫽17, ⌫⫽960, and p ⫽972 cm⫺1. Both reflection minima are determined by the carrier density, n f . Neglecting the free-carrier damping ␥, the reflectivity R⫽ 关 (n⫺1) 2 ⫹k 2 兴 / 关 (n⫹1) 2 ⫹k 2 兴 is a minimum when equals 1. Setting ⫽1, the two roots, ⫾ , of Eq. 共1兲 are given by11
0 共 1⫹ 2p / L2 兲 ⫺1⫾ 兵 关 0 共 1⫹ 2p / L2 兲 ⫺1 兴 2 ⫺4 0 共 ⬁ ⫺1 兲 2p / L2 其 1/2 2 共 ⬁ ⫺1 兲 / T2
冉
2p L2 ⫺ T2 1⫺ 2 ⫹ , ⫹i ␥ T2 ⫺ 2 ⫺i ⌫
共2兲
,
transmission spectrum of the GaN nanowires to that of the quartz substrate. The transmission spectrum of the bulk GaN, taken from the work by Ivantsov et al.,14 is also displayed for comparison. The transmission is high in the low-energy region and decreases gradually with increasing frequency. The transmission begins to decline rapidly around E ⫽3.3 eV, indicating the onset of fundamental absorption. The transmission reaches a minimum at E⫽3.65 eV, which corresponds to the absorption edge. In contrast, the absorption edge of the bulk GaN, as shown in Fig. 3, is 3.45 eV. The absorption edge of the GaN nanowires is blueshifted by 0.2 eV, or approximately 6%, from the bulk edge. The shift of the band gap with the nanowire radius R, is assumed to follow the expression,15,16 ⌬E⫽E 共 R 兲 ⫺E g 共 bulk兲 ⬇
冋
册
2ប 2 1 1 1.8e 2 , ⫹ ⫺ 2 2R m e m h ⬁R
共3兲
where m e and m h are the effective mass of electron and hole, respectively, and ⬁ is the high-frequency dielectric constant. Using the bulk parameters: m e ⫽0.19, m h ⫽0.60, and ⬁ ⫽5.35, the energy shift ⌬E⫽0.2 eV, corresponds to a radius, R⬵2.5 nm. The estimated radius R, represents the average radius of variously sized nanowires. The GaN nanowires examined herein are in the strong confinement regime, since R is much smaller than the exciton Bohr radius a B of bulk GaN 共⬇11 nm兲.17 Notably, the absorption spectral width from the onset 共3.3 eV兲 to the edge 共3.65 eV兲 is broader than the width of the spectrum corresponding to the bulk sample, revealing dispersion in nanowire diameter. Figure 4 depicts the temperature dependence of the energy gap, E g . This dependence was deduced using the Varshni empirical equation18 E g (T)⫽E g (0)⫺ ␣ T 2 /(  ⫹T), where E g (0) is the energy gap at 0 K, and ␣ and  are
FIG. 3. Transmission spectrum 共solid line兲 of GaN nanowires. For comparison, the transmission spectrum of bulk GaN 共dashed line兲, taken from Ref. 14, is also plotted. Downloaded 24 Nov 2006 to 140.120.80.11. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
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In conclusion, this study has examined the optical properties of GaN nanowires. The energy gap of the GaN exhibits a blueshift from the bulk gap. The temperature effect of the energy gap is weaker in the GaN nanowires than in the bulk. The infrared response can be used to evaluate free-carrier density in GaN nanowires.
S. Nakamura, T. Mukai, and M. Senoh, Appl. Phys. Lett. 64, 1687 共1994兲. S. Strite and H. Morkoc, J. Vac. Sci. Technol. B 10, 1237 共1992兲, and references therein. 3 S. Nakamua, S. Peartan, and G. Fasol, The Blue Laser Diode, 2nd edition 共Springer, Berlin, 2000兲. 4 W. Han, S. Fan, Q. Li, and Y. Hu, Science 277, 1287 共1997兲. 5 G. S. Cheng, L. D. Zhang, Y. Zhu, G. T. Fei, L. Li, C. M. Mo, and Y. Q. Mao, Appl. Phys. Lett. 75, 2455 共1999兲; G. S. Cheng, L. D. Zhang, S. H. Chen, Y. Li, L. Li, X. G. Zhu, Y. Zhu, G. T. Fei, and Y. Q. Mao, J. Mater. Res. 15, 347 共2000兲. 6 C. C. Tang, S. S. Fan, M. L. de la Chapelle, and P. Li, Chem. Phys. Lett. 333, 12 共2001兲. 7 B. O. Dabousi, J. Rodriguez-Viejo, F. M. Midulec, J. R. Heine, H. Mattoussi, R. Ober, K. F. Jensen, and M. G. Bawendi, J. Phys. Chem. B 101, 9463 共1997兲. 8 C.-C. Chen and C.-C. Yeh, Adv. Mater. 12, 738 共2000兲. 9 C.-C. Chen, C.-C. Yeh, C.-H. Ho, M.-Y. Yu, H.-L. Liu, J.-J. Wu, K.-H. Chen, J.-Y. Peng, and Y.-F. Chen, J. Am. Chem. Soc. 123, 2791 共2001兲. 10 H. Siegle, L. Eckey, A. Hoffman, C. Thomsen, B. K. Meyer, D. Schikora, M. Hankeln, and K. Lischka, Solid State Commun. 96, 943 共1995兲. 11 R. T. Holm, P. H. Klein, and P. E. R. Nordquist, Jr., J. Appl. Phys. 60, 1479 共1986兲. 12 H.-L. Liu, C.-C. Chen, C.-T. Chia, C.-C. Yeh, C.-H. Chen, M. Y. Yu, S. Keller, and S. P. DenBaars, Chem. Phys. Lett. 345, 245 共2001兲. 13 H. M. Chen, Y. F. Chen, M. C. Lee, and M. S. Feng, Phys. Rev. B 56, 6942 共1997兲. 14 V. A. Ivantsov, V. A. Sukhoveev, V. I. Nilokaev, I. P. Nikitina, and A. A. Dmitriev, Phys. Solid State 39, 763 共1997兲. 15 R. Rossetti, S. Nakahara, and L. Brus, J. Chem. Phys. 79, 1086 共1983兲; L. Brus, J. Chem. Phys. 80, 4403 共1984兲. 16 Y. Kayanuma, Solid State Commun. 59, 405 共1986兲. 17 Y. Xie, Y. Qian, W. Wang, S. Zhang, and Y. Zhang, Science 272, 1926 共1996兲. 18 Y. P. Varshni, Physica 共Amsterdam兲 34, 149 共1967兲. 19 W. Shan, T. Schmidt, X. H. Yang, J. J. Song, and B. Goldenberg, J. Appl. Phys. 79, 3691 共1996兲. 1 2
FIG. 4. Temperature dependence of the energy gap for GaN nanowires.
constants. The best fit, shown as the solid line in Fig. 4, yields E g (0)⫽3.724 eV, ␣ ⫽9.97⫻10⫺4 eV/K, and  ⫽861 K. The change in gap energy from 300 to 0 K is ⌬E g ⫽E g (0)⫺E g (300 K)⫽0.075 eV. In the bulk GaN, the corresponding change is ⌬E g ⫽0.086 eV. 19 The temperature effect on the energy gap is therefore slightly weaker in the nanowires than in the bulk material. Determining free-carrier density from the infrared reflectance minima is an extremely useful method in research on nanostructured semiconductors. The carrier density of a semiconductor is normally estimated using conventional transport measurements. However, due to the small size, electrical contacts cannot easily be put into nanowires, making transport measurements difficult. The infrared reflection technique is nondestructive, easy to perform, and the results are simple to analyze. In addition, free-carriers are conduction electrons thermally ionized from donors according to n f ⬀N 1/2 d exp(⫺Ed/2k B T), where E d and N d are the ionization energy and concentration of donors, respectively. The freecarrier density n f can then be used to deduce the concentration of donors N d , an extremely important parameter for semiconductors.
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