Refractive index of a single ZnO microwire at high temperatures Kangsheng Qiu, Yanhui Zhao, Yunan Gao, Xiangbo Liu, Xiaofan Ji, Shuo Cao, Jing Tang, Yue Sun, Dongxiang Zhang, Baohua Feng, and Xiulai Xu Citation: Applied Physics Letters 104, 081109 (2014); doi: 10.1063/1.4866668 View online: http://dx.doi.org/10.1063/1.4866668 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Ag/ZnO hybrid systems studied with scanning tunnelling microscopy-based luminescence spectroscopy J. Appl. Phys. 119, 095310 (2016); 10.1063/1.4943070 Effect of Mg diffusion on photoluminescence spectra of MgZnO/ZnO bi-layers annealed at different temperatures J. Appl. Phys. 114, 183103 (2013); 10.1063/1.4830010 Relaxor- and phase-transition-like behaviors in ZnO single crystals at high temperatures Appl. Phys. Lett. 102, 112907 (2013); 10.1063/1.4796136 Structural and photoluminescence properties of Gd implanted ZnO single crystals J. Appl. Phys. 110, 033534 (2011); 10.1063/1.3619852 Microphotoluminescence investigation on single ZnO microrods with different morphologies J. Appl. Phys. 105, 123109 (2009); 10.1063/1.3153120 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 159.226.35.154 On: Mon, 20 Jun 2016 01:27:18
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Refractive index of a single ZnO microwire at high temperaturesKangsheng Qiu, Yanhui Zhao, Yunan Gao, Xiangbo Liu, Xiaofan Ji, Shuo Cao, Jing Tang, Yue Sun, DongxiangZhang, Baohua Feng, and Xiulai Xu Citation: Applied Physics Letters 104, 081109 (2014); doi: 10.1063/1.4866668 View online: http://dx.doi.org/10.1063/1.4866668 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Ag/ZnO hybrid systems studied with scanning tunnelling microscopy-based luminescence spectroscopy J. Appl. Phys. 119, 095310 (2016); 10.1063/1.4943070 Effect of Mg diffusion on photoluminescence spectra of MgZnO/ZnO bi-layers annealed at different temperatures J. Appl. Phys. 114, 183103 (2013); 10.1063/1.4830010 Relaxor- and phase-transition-like behaviors in ZnO single crystals at high temperatures Appl. Phys. Lett. 102, 112907 (2013); 10.1063/1.4796136 Structural and photoluminescence properties of Gd implanted ZnO single crystals J. Appl. Phys. 110, 033534 (2011); 10.1063/1.3619852 Microphotoluminescence investigation on single ZnO microrods with different morphologies J. Appl. Phys. 105, 123109 (2009); 10.1063/1.3153120
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 159.226.35.154 On: Mon, 20 Jun 2016
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 159.226.35.154 On: Mon, 20 Jun 2016
where R is the side length of the hexagonal cavity, k is the
resonance wavelength, n is the refractive index, and N is the
mode number. The factor b is related to the polarization of
the spectrum, b ¼ n for TE polarized modes and b ¼ 1=n for
TM. At room temperature, the mode number N of WGMs is
determined by the refractive index from the reference.13
When the temperature rises from 300 K to 400 K, the WGMs
shift to the low energy and keep the same mode number. The
thermal expansion of the microwire can be neglected;12
therefore, the side length R can be considered as a constant.
The resonant wavelengths can be read from the sharp peaks
in PL spectra from Fig. 2, which results in that the refractive
index can be calculated with Eq. (1).
It is well known that ZnO is a birefringence material,
and the refractive indexes of TE and TM modes are different.
The refractive indexes as a function of wavelength at differ-
ent temperatures for TE polarized PL (no) and the TM polar-
ized PL (ne) are shown in Fig. 3. In Figs. 3(a) and 3(c), the
refractive index of TE mode is greater than that of TM
mode, namely, no > ne. This means that it is a negative uni-
axial crystal in the UV range. However, in Figs. 3(b) and
3(d), the refractive index of TM polarized PL is greater
(no < neÞ, indicating a positive uniaxial crystal in the visible
FIG. 1. (a) SEM image of an individual ZnO microwire, the white bar is
about 5 lm in length. The inset shows the path way of WGMs in a microcav-
ity. (b) The TE and TM polarized PL spectra of the ZnO microwire at room
temperature. (c) The enlarged PL spectra from 380 nm to 430 nm for the two
polarized modes.
FIG. 2. Normalized TE polarized PL spectra in the UV range (a) and in the
visible range (b) at different temperatures. The gray arrows mark the red
shift with increasing temperature. Each spectrum is shifted for clarity.
081109-2 Qiu et al. Appl. Phys. Lett. 104, 081109 (2014)
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01:27:18
range. It can be seen that the ZnO single crystal microwire is
not always a positive or negative uniaxial crystal, but
depends on the wavelength.13 In addition, the refractive
index in UV range is greater than that in the visible range for
both TE and TM polarized PL spectra. The dispersion curves
for TE and TM polarized PL spectra move up monotonically,
providing a refractive index increase of ZnO microwire with
increasing temperature.
From the refractive index change in Fig. 3, the tempera-
ture dependent refractive index at fixed wavelengths can be
deduced using cubic spline interpolation. Figure 4 shows
that the refractive index increases at fixed wavelengths when
the temperature increases from 299.7 K to 399.8 K. The re-
fractive index increases faster in the UV range than that in
the visible range for both TE and TM polarized PL. For
example, at 400 nm, the refractive indexes increase by 0.042
and 0.053 for the TE and TM polarized PL, respectively.
While in the visible range, the refractive index increase is
about 0.013, which is around 1/3 of that in the UV range for
both TE and TM modes. The refractive index nðxÞ is related
to the relative dielectric constant �rðxÞ derived from the
Maxwell’s equations: n xð Þ ¼ffiffiffiffiffiffiffiffiffiffiffi�rðxÞ
p. For the ZnO mate-
rial, the permittivity can be expressed by the Lorentz oscilla-
tor model.32 The optical dielectric function � xð Þ is given by
the following expression:
� xð Þ ¼ �0s þe2
�0m
Xn
Neb;n
ðx2n � x2Þ � icnx2
; (2)
where x is the angular frequency, Neb;n is the concentration
of electrons, xn is resonance frequency, cn is the frictional
constant, �0 is the permittivity of vacuum, e and m are the
charge and mass of a single electron. �0s represents the con-
tributions to � from electronic resonances with xn at a high
frequency range, which equals to 1 here. When the tempera-
ture is the only variable, the dielectric function in the
Lorentz oscillator model can be simplified as
� xð Þ� 1=ðx2n � x2Þ. The resonance frequency xn corre-
sponds to the exciton energy, which shows a redshift as the
temperature rises, as aforementioned. As a result, the permit-
tivity � xð Þ increases as the temperature rises. The UV light
frequency is closer to resonant frequency than the light in the
visible range, which results in that the refractive index
changes faster with increasing temperature. As the other pa-
rameters in Eq. (2) are not determined accurately, the refrac-
tive index changes as a function of temperature can only be
explained qualitatively here.
In summary, the refractive indexes of wurtzite ZnO sin-
gle microwire of TE and TM polarized PL were extracted
precisely according to the redshifts of the WGMs in a tem-
perature range from 300 K to 400 K. The birefringence prop-
erties of the single ZnO microwire depend on the
wavelength range. With increasing temperature, the reso-
nance frequencies red shift as the energy gap narrowing in
ZnO microwire. According to the Lorentz oscillator model,
the refractive index of ZnO increases as the temperature
rises. The refractive index increases more in UV range,
which is due to these cavity modes are close to the resonance
frequencies. The refractive index of ZnO microwires in this
work provides a fundamental parameter to understand the
microstructure-based strong coupled cavities, UV lasers and
nonlinear optics at high temperatures.
This work was supported by the National Basic Research
Program of China under Grant Nos. 2013CB328706,
2014CB921003, and 2013CB632704; the National Natural
Science Foundation of China under Grant Nos. 11174356 and
61275060; the Hundred Talents Program of the Chinese
Academy of Sciences; and the China Postdoctoral Science
Foundation under Grant No. 2013M540155.
FIG. 3. The dispersion curves of the TE modes (a) and (b) and TM modes
(c) and (d) as a function of temperature in the UV and the visible ranges.
FIG. 4. The refractive index change as a function of temperature for both TE
(a) and TM (b) modes. The refractive index at 300 K is used as reference.
081109-3 Qiu et al. Appl. Phys. Lett. 104, 081109 (2014)
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