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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

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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,a) and Xiulai Xua)

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences,Beijing 100190, People’s Republic of China

(Received 11 January 2014; accepted 11 February 2014; published online 25 February 2014)

We report a study of refractive index of a wurtzite ZnO single crystal microwire at a temperature

range from room temperature to about 400 K using optical cavity modes. The photoluminescence (PL)

spectra of the ZnO microwire at different temperatures were performed using a confocal

micro-photoluminescence setup. The whispering gallery modes observed in the PL spectra show a

redshift both in the ultraviolet and the visible range as the temperature rises. The redshift is used to

extract the refractive index of the ZnO microwire. The dispersion relations are deduced at different

temperatures, and the results show that the refractive index increases with raising temperature for both

transverse electric and transverse magnetic modes. The refractive index increases faster at a shorter

wavelength, which is due to the fact that the shorter wavelength is closer to the resonance frequencies

of ZnO microwire according to the Lorentz oscillator model. VC 2014 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4866668]

Single ZnO microwire microcavities have attracted much

attention for their potential applications, such as photolumi-

nescence enhancement,1,2 polariton condensation,3 and

ultraviolet (UV) lasers.4–10 Several types of cavity modes

have been observed in ZnO micro structures, including whis-

pering gallery modes (WGMs),11,12 quasi-WGMs,13–15 and

Fabry-Perot modes (FPMs).16,17 The WGMs have higher qual-

ity factors (Q) as they are the resonances of the cavity by the

total internal reflection,6,11,18–22 while the quasi-WGMs and

FPMs formed from the partial reflection have lower quality

factors.2,14,23,24 Due to the strong coupling between the exci-

tons and the cavity modes, exciton-polariton has been

observed in WGMs, quasi-WGMs, and FPMs, but the UV

lasering was studied mainly in WGMs due to the higher qual-

ity factors.7,25–29

Since ZnO material has a large exciton binding energy of

about 60 meV, exciton-polariton emission has been observed

at room temperature or even higher.17,30 In order to obtain the

energy-wavevector (E-k) dispersion relation of exciton-

polariton, the dispersion relation of the refractive index must

be obtained first. For bulk materials or thin films, the refrac-

tive indexes were characterized traditionally using methods,

such as transmission, reflectivity, or ellipsometry spectros-

copy.31,32 However, it is very difficult to use these methods to

measure the refractive index of a single microwire. In addi-

tion, the refractive index of ZnO above the room temperature

has been rarely studied. In this letter, the refractive indexes of

ZnO at a temperature within the range of 300 K–400 K are

reported. The WGMs at different temperatures above 300 K

were mapped using confocal micro-photoluminescence

(l-PL) spectroscopy, and from the PL spectra the refractive

indexes of a single ZnO microwire are extracted.

The ZnO microwires were grown by a vapor phase

transport method using high-temperature tube furnace.33,34 A

quartz boat filled with a mixture of ZnO and graphite powder

(weight-ratio, 1:1) was placed at the end of a slender

one-end sealed quartz tube, and several cleaned Si substrates

on a quartz wafer were placed in the quartz tube about 10 cm

away from the quartz boat. The furnace was pre-heated and

maintained at 950 �C, the quartz tube was then pushed into

the furnace for a 8-h reaction. After that the tube was pulled

out and cooled down to the room temperature at a rate of

30 �C/min. The Si substrates were then covered with a lot of

crystal whisker which was confirmed to be the wurtzite

structured ZnO microwires using scanning electron micro-

scope (SEM) and X-Ray Powder Diffraction. For the PL

studies, a single hexagonal ZnO microwire was transferred

to a Si substrate, and the sample was placed in a continuous-

flow cryostat with a pressure under 10�5 millibars and a tem-

perature within the range of 300 K–400 K. A continuous

wave He-Cd laser at 325 nm was used as an excitation

source. The pump laser light was focused by a 36� reflective

microscope objective with a spot size of about 2 lm in diam-

eter. The PL from the ZnO microwire was collected by the

same objective and dispersed through a 0.55 m monochroma-

tor, then detected by a nitrogen-cooled, back-illuminated

charge-coupled device (CCD) camera. The transverse elec-

tric (TE, E?c-axis) and transverse magnetic (TM, E//c-axis)

polarized PL spectra were separated by placing a

Glan-Taylor polarizer in front of the monochromator.

Figure 1(a) presents a SEM image of the ZnO microwire

studied in this work. The diameter of the ZnO microwire is

about 9.5 lm. The TE and TM polarized PL spectra of the

ZnO single microwire are shown in Fig. 1(b). For the TE

polarized PL spectrum, two main peaks in the UV range are

centered at about 380 nm and 391 nm with a full width at

half maximum (FWHM) of 5 nm and 20 nm, respectively.

The PL in the UV range is due to the emission of excitons in

the ZnO microwire.35 The wurtzite ZnO conduction band is

s-like with a C7 symmetry, while the valence band is p like

state and split into three bands due to the crystal-field and

the spin-orbit interaction induced splitting. The excitons cor-

responding to the three valence bands are usually denoted

by A, B, and C, with the symmetries of C9, C7, and C7,a)Electronic addresses: [email protected] and [email protected]

0003-6951/2014/104(8)/081109/4/$30.00 VC 2014 AIP Publishing LLC104, 081109-1

APPLIED PHYSICS LETTERS 104, 081109 (2014)

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01:27:18

respectively.36 According to the selection rules of transitions,

all three exciton transitions are allowed in the r polarization

(E?c axis, and k?c axis), but C exciton is quite weakly to

be observed. The C excitonic transition is strongly allowed

in the p polarization (E//c, k?c), while the transitions for A

exciton is forbidden and the B exciton is only weakly observ-

able in this geometry.35 As a result, the TE polarized PL in-

tensity is stronger than that of TM in the UV range. In

addition, the broad peak in the visible range from 430 nm to

730 nm is centered at about 600 nm with a FWHM of about

240 nm, which is due to the defect-related emission.37–40 In

this range, the TM polarized PL is stronger than TE, as the

WGMs in ZnO microwires are preferentially TM

polarized.41

On top of the main peaks in the PL spectra, periodically

spaced small peaks can be observed clearly from the UV to

the visible range, which are ascribed to the WGMs,11 as

sketched in the inset in Fig. 1(a). In the visible range the

WGMs can be clearly observed in Fig. 1(b), and in the UV

range they appear very densely but still can be resolved.

Figure 1(c) shows the enlarged spectra in the UV range. The

peak intervals of WGMs become larger as the wavelength

increases, which are similar to what have been observed

before.24

Figs. 2(a) and 2(b) show the temperature dependent PL

spectra of TE polarized modes in the UV and the visible

range, respectively. The TM polarized PL spectra at different

temperatures are similar to that of TE, and not shown here.

The excitonic peaks and the optical WGMs shift to red as the

temperature increases from 299.7 K to 399.8 K. A difference

is that exciton energy red shifted by 75 meV, while the

WGM at 402 nm only shifted about 27 meV for the TE polar-

ized PL as marked in Figure 2(a). The redshift for the main

peak in the UV range is due to the band gap narrowing of

ZnO, while that for the optical WGMs is due to the refractive

index increase of ZnO microwire when the temperature

rises.28 From the redshift of WGMs, the temperature depend-

ent refractive indexes of ZnO microwire can be extracted

precisely. The mode equation for the WGMs in a regular

hexagonal cavity is24

R ¼ k

3ffiffiffi3p

nNþ 6

parctanðb

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3n2 � 4p

Þ� �

; (1)

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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01:27:18

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