The e
ffect of thermal annealing on the optical and
electrical properties of ZnO epitaxial
films grown
on n-GaAs (001)
Wei-Rein Liu,*aBi-Hsuan Lin,aChi-Yuan Lin,bSong Yang,aChin-Chia Kuo,b Forest Shih-Sen Chien,cChen-Shiung Chang,bChia-Hung Hsu*ab
and Wen-Feng Hsiehb
Wurtzite ZnO epitaxial layers grown on n-type GaAs (001) by pulsed laser deposition (PLD) exhibited n-type conductivity. Post-growth annealing leads the conversion of carrier type from electron to hole, as revealed by Hall effect measurements, although only moderate structural improvement was observed. The carrier type conversion is attributed to thermally activated arsenic diffusion from the substrate, confirmed by secondary ion mass spectrometry and photoluminescence. The surface electrical properties of both the as-deposited n-type and annealed p-type ZnO epitaxial layers were thoroughly characterized by Kelvin force microscopy (KFM) and electrostatic force microscopy (EFM). The results indicated the existence of a high density of surface states close to the ZnO midgap with a density of a few 1014cm2eV1. The Fermi levels (EF) of n- and p-type ZnO epitaxial layers were found to be 1.06 eV below the conduction-band minimum (CBM) and 1.612–1.769 eV above the valence-band maximum (VBM), respectively. The small EFdifference between the n- and p-type ZnO epitaxial layers implies Fermi level pinning at the surface of both n- and p-type ZnO epitaxial layers.
Introduction
ZnO, a II–VI compound semiconductor, is a promising material for high efficiency light-emitting devices and for optical appli-cations in UV luminescence due to its wide direct band gap, 3.37 eV, and large exciton binding energy, 60 meV at 295 K. However, because of the asymmetric doping limitations and the compensation effect caused by native defects, such as Oiand
VZn which play a role as hole killer, reliable p-type ZnO is
difficult to attain.1,2How to fabricate high quality and stable
p-type ZnO epitaxiallms thus remains the major obstacle to the realization of ZnO-based photoelectronic devices.
To achieve p-type ZnO, various doping approaches, such as group V elements (N,3P,4As,5and Sb6) substituting for O, group I elements (Li7and Ag8) for Zn, donor–acceptor co-doping, with group III and group V elements simultaneous substituting for Zn and O,9and dual-acceptor co-doping, with group I and group
V elements substituting for Zn and O simultaneously,10 have
been explored in recent years. Among these approaches, the most promising dopant for p-type ZnO is group V elements. Ryu
et al.5 reported that ZnO layer grown on GaAs substrate exhibited p-type conductivity aer post-growth annealing and ascribed the conductivity conversion to the diffusion of As atoms from the substrate into ZnOlms. ZnO homojunction light emitting diode with As-doped ZnO as the p-type material has also been demonstrated.5,11Kang et al.12ascribed the p-type conductivity of As-doped ZnOlms to the existence of AsZn–2VZn
complex, whose acceptor binding energy is 0.1455 eV deter-mined by using photoluminescence. This value is in good agreement with what reported by Limpijumnong et al.13based
onrst-principles calculations.
It is known that surface electrical properties of ZnO could play a crucial role in its overall electrical characteristics. Surface states formed at ZnO surface due to surface atomic recon-struction, structural defects, adsorbates, etc.; all may contribute to its electrical properties. For example, Allen et al.14reported that the existence of oxygen vacancies (VO) tended to pin
Fermi-level close to VO(+2,0) defect level, which is approximately 0.7 eV
below the conduction band minimum, in their studies of Zn-polar face of ZnO wafers. Knowledge about surface electrical properties is thus important for the interpretation of the elec-trical behavior of ZnO. Nevertheless, only a few studies about the surface electrical properties of p-type ZnO layers have been reported.
In this work, we studied the conductivity conversion of ZnO epitaxial layers grown by pulsed laser deposition on n-type GaAs (001) substrates upon thermal annealing. Structural
aDivision of Scientic Research, National Synchrotron Radiation Research Center,
Hsinchu 30076, Taiwan. E-mail: liu.weirein@nsrrc.org.tw; chsu@nsrrc.org.tw; Fax: +886 3 578 3813; Tel: +886 3 578 0281 ext. 7130/7118
bDepartment of Photonics and Institute of Electro-Optical Engineering, National Chiao
Tung University, Hsinchu 30010, Taiwan
cDepartment of Physics, Tunghai University, Taichung 40704, Taiwan
Cite this: RSC Adv., 2015, 5, 12358
Received 4th November 2014 Accepted 15th January 2015 DOI: 10.1039/c4ra13771j www.rsc.org/advances
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investigation of the as-grown and thermally annealed ZnOlms were performed by using X-ray diffraction (XRD); carrier conductivity were conducted by Hall measurement. Secondary ion mass spectrometry (SIMS), and photoluminescence (PL) were employed to characterize the doping species. The spatially resolved surface electrical properties of n- and p-type ZnO epitaxial layers were explored by Kelvin force microscopy (KFM) and electrostatic force microscopy (EFM). The results elucidated the existence of a considerable amount of surface states which played an important role in the electrical properties of the ZnO layers.
Experimental section
ZnO epitaxial lms were deposited on Si doped n-type GaAs (001) substrate by pulsed laser deposition (PLD). A beam out of a KrF excimer laser (l ¼ 248 nm) at a repetition rate of 10 Hz was focused to produce an energy density 5–7 J cm2 on a commercial hot-pressed stoichiometric ZnO (5 N) target.15The lms were deposited at substrate temperature held between 300 and 600C without introducing oxygen gasow; the growth rate is0.56 ˚A s1and the ZnO layer thickness is400 nm. Learning from our previous studies on ZnO lms grown on GaAs (111), annealing temperature above 500C was necessary to trigger the conversion of carrier type. Similar results have also been reported by other groups.5,16On the other hand, annealing at 700 C or higher leads to serious degradation of surface morphology. This phenomenon is attributed to the serious liberation of As from GaAs substrate, which is conrmed by composition analysis using scanning electron microscopy equipped with energy dispersive spectrometer. Therefore, the annealing temperature of all the samples presented in this work wasxed at 600C.
XRD measurements were performed using a four-circle diffractometer at beamline BL13A of the National Synchrotron Radiation Research Center, Taiwan with a wavelength of 1.024 ˚A. Two pairs of slits located between the sample and the detector yielded a resolution of better than 4 103 ˚A1. Chemical depth prole of the samples was examined by an Atomika SIMS 4500 using Cs+as the primary ions and an impact energy of 15 keV. The carrier characteristics of the samples were measured by Hall effect measurements using the four-probe van der Pauw conguration at room temperature (RT). PL measurements were carried out using a He–Cd laser with a wavelength of 325 nm as the pumping source; the emitted light was dispersed by a Triax-320 spectrometer and detected by an UV-sensitive photomultiplier tube. The spatially resolved elec-trical properties of the ZnO epitaxial layers were characterized by KFM and EFM. A commercial closed-loop-scanner Scanning Probe Microscopy (SPM, Vecco Innova) with a Cr/Pt-coated cantilever, operating in li-mode with a two-pass technique and dual-frequency mode was employed. An oscillating signal Vapplied ¼ Vaccos(ut) with an amplitude Vac of 3.5 V and a
frequency of 18.72 kHz was applied to the tip; a li height of 50 nm was used to reduce mechanical-force effect on tip and to remove articial signals in electric measurements.
In both KFM and EFM measurements, an oscillating voltage Vappliedis applied directly to the AFM tip and a bias Vsampleis
applied to sample. The tip feels an electrostatic force
Fu¼vCvzðVsample VSÞVapplied, where vCvz and VSare the vertical
derivative of the capacitance and surface potential difference between sample and tip, respectively. KFM measures VS by
adjusting Vsample on the tip to minimize Fu.17 Quantitative
voltage measurements are made by recording the effective VSas
a function of tip position. On the other hand, an EFM image is made of Fuamplitude recorded as a function of tip position
with axed Vsample. VS at any location is given by the Vsample
corresponding to the minimum in the local Fu vs. Vsample
curve.17,18For convenient discussion and the consistence of VS
determined from EFM and KFM results in following sections, KFM images are inversed because of the opposite polarity of applied bias in KFM and EFM measurements.
Results and discussion
Fig. 1(a) illustrates an XRDq–2q radial scan along the surface normal of the ZnO layer grown on n-GaAs (001) at 500 C
Fig. 1 (a) An XRD radial scan along the surface normal of the ZnO layer grown on n-GaAs (001) at 500C followed by post-growth annealing at 600 C. The inset shows a q-rocking curve across ZnO (0002) reflection, (b) XRD scans across ZnO (1011) and GaAs (111) off-normal reflections of the ZnO layer.
followed by post-growth annealing at 600C. Only ZnO (0002), (0004), and (0006) reections together with the GaAs (002), (004), and (006) reections were observed, elucidating the ZnO layer is c-plane oriented with its [0001] axis parallel to GaAs [001] direction. The mosaicity with a full-width at half-maximum (FWHM) of 1.04, derived from the ZnO (0002)q-rocking curve shown in the inset of Fig. 1(a), reveals good crystalline quality of the ZnO layer along the growth direction. The intensity prole of the azimuthalf-scans across ZnO (1011) and GaAs (111) off-normal reections of the same sample are depicted in Fig. 1(b). Six evenly spaced ZnO {1011} diffraction peaks conrm that the ZnOlm has 6-fold rotational symmetry against surface normal and is epitaxially grown on GaAs (001). The twist angle (12.7), derived from the FWHM of the azimuthalf-scan across the ZnO {1011} reection, is much worse than that of c-ZnO grown on (111) oriented GaAs, reecting the unfavorable inuence of symmetry mismatch on epitaxial growth. From the angular coincidence of the ZnO (1011) reection with that of the GaAs (110) reection, we determined the relative orientation between ZnO and GaAs as (0001)[1010]ZnOk(001)[110]GaAs. Because the
surface projection of Ga and As dangling bonds are perpen-dicular to each other on the GaAs (001) surface, the surface anisotropy eliminates the formation of the second rotational variant with 90in-plane rotation.19As to the atomic
arrange-ment on the ZnO/GaAs interface, it requires further investiga-tion and is beyond the scope of this work. Samples grown at different temperatures all showed the same epitaxial orienta-tion. The twist angle decreased monotonically with increasing growth temperature from 300 to 600C. The tilt angle, repre-sented by the FWHM of theq-rocking curve across the ZnO (0002) reection, also decreased with elevated temperature initially, reached a minimum at500C, and then increased as grown at 600C. In terms of the quality of crystalline structure, the sample grown at 500C had the smallest tilt angle and the second smallest twist angle; the one grown at 600C had the smallest twist angle and the second smallest tilt angle among all the samples measured. In addition, the one grown at 500C had the better electrical properties, larger carrier density, higher mobility, and low resistivity, than the 600 C one. We thus selected 500C grown sample for further optical and electrical studies.
Bytting the angular positions of many Bragg reections, the lattice parameters of the ZnO layer grown at 500C was determined to be a¼ 3.252 ˚A and c ¼ 5.203 ˚A. As compared with the bulk values, a¼ 3.249 ˚A and c ¼ 5.206 ˚A determined from a ZnO wafer, the ZnO epitaxiallm was almost strain free. The strain of c-plane ZnO grown on GaAs is signicantly smaller than those grown on c-plane sapphire and Si (111) by the same method, which may be attributed to the smaller mismatch in thermal expansion coefficients between ZnO (6.5 106K1)
and GaAs (5.39 106K1). Hall effect measurements of the as-deposited samples revealed that electrons were the dominant carriers in all these samples. For the 500C grown sample, its carrier density, mobility and resistivity are 5.78 1018 cm3, 24.2 cm2V1s1, and 4.4 102U cm, respectively.
Aer thermal annealing at 600C for one hour, the crys-talline quality of the ZnO layers exhibited minor
improvement, tilt angle ¼ 0.91and twist angle ¼ 11.8, as revealed by XRD measurements but the Hall effect results showed drastic changes. The dominant carriers switched to holes for all the annealed samples. The hole concentration, hole mobility, and resistivity of the ZnO layer annealed at 600C are 7.6 1018cm3, 24.6 cm2V1s1and 3.3 102U
cm, respectively. It is obvious that thermal annealing leads to the conductivity conversion from n- to p-type for the ZnO layers grown on GaAs.
To investigate the cause of conductivity switching and the possible element responsible for such a conversion, we con-ducted dynamic SIMS measurement on the 600 C annealed ZnO layer. The secondary ion intensity as a function of depth from the ZnO surface is depicted in Fig. 2. Because the relative sensitive factors of Ga and As in ZnO matrix as well as Zn and O in GaAs matrix are not available in database, we could not quantitatively deduce the concentration of these elements but only probed the trend of concentration variation of individual element. From the steep decrease of the SIMS intensities of various elements, we derived the ZnO layer thickness410 nm, which agreed well with the thickness estimated from the growth rate and deposition time. Theat concentration proles of As and Ga throughout the lm manifested their uniform distri-bution in the ZnO layer. Biswas et al. conducted a thorough study on the diffusion behavior of As and Ga from GaAs substrate into MOCVD-grown ZnO lms upon post-growth annealing.20They found As diffusion prevailed over Ga in the samples annealed at 600 and 700C and the observed p-type conductivity was attributed to the As-related acceptors (AsZn–2VZn complex). For the sample annealed at 800C, Ga
atoms diffused more than As atoms and they formed shallow donor complex, GaZn, compensating the p-type carriers and
leading to the reversion of conductivity to n-type. The SIMS results and electrical characteristics of our 600 C annealed sample resemble that of the 600–700 C annealed samples reported by Biswas, implying that the change of the electrical properties in our case is mainly ascribed to the diffusion of As atoms. To verify this speculation, we conducted optical and SPM measurements.
Fig. 2 SIMS depth profile of the ZnO layer grown on n-GaAs (001) at 500C followed by post-growth annealing at 600C.
The optical properties of the as-deposited and annealed ZnO lms were characterized by PL measurements conducted at 13 K, as shown in Fig. 3(a). The spectrum of the as-deposited ZnO has a dominant center peak at 3.362 eV, ascribed to the emission of donor-bound exciton (D0X). Aer annealing, the
dominant emission was red shied by 9 meV to 3.353 eV, which was attributed to the acceptor-bound exciton (A0X).21The
red shiing of the near-band edge emission was also reported by other groups and can be regarded as a signature of carrier type conversion.5,11The small emission peak at 3.309 eV in the
annealed sample was identied as the transition from free electrons to the acceptor state (FA). Acceptor binding energy (ionization energy) can be derived according to EA¼ Eg EFA+
kT/2, where Eg¼ 3.437 eV is the intrinsic band gap of ZnO,22and
EFA¼ 3.309 eV is the free electron-acceptor level transition at
13 K. The acceptor binding energy so obtained, 127 meV, agrees well with that of AsZn–2VZn complex determined by both
experimental measurements8 and rst principles calculations (150 meV) based on density functional theory with local density approximation and ultraso pseudopotentials.12 This
result indicates that AsZn–2VZncomplex formed by means of
thermal annealing plays an important role in the conversion of carrier type and the change of emission mechanism. The peaks at 3.23 and 3.158 eV are originated from the donor–acceptor
pair (DAP) transition and the associated single phonon replica (DAP-1LO).5,8,23
To identify the nature of the transition at 3.353 eV, temperature-dependent PL measurements of the annealed ZnO layer was performed and the spectra of near-band edge region are depicted in Fig. 2(c). Bytting the peak positions of the A0X
emission with the Varshni's formula,24 we determined the
binding energy of the A0X transition to be14 meV. This value is larger than the binding energy of D0X (10 meV) emission, determined from the as-deposited n-type ZnO layer, implying the faster attenuation of D0X intensity than A0X intensity with rising temperature due to thermally activated dissociation.
To understand the inuence of dopants on the surface potential of ZnO epi-layers, we performed both KFM and EFM measurements. Prior KFM measurements, the work function of SPM tip,FPt, was calibrated to be 5.650 eV by using a0.48 mm
thick Ptlm grown on glass as a reference. The conventional topographic images of the as-deposited n-type and annealed p-type ZnO layers, shown in Fig. 4(a) and (c), yielded root mean square roughnesses 18.7 nm and 11.9 nm, respectively. The smaller surface roughness of the p-type ZnO layer manifests the improvement of surface planarization by post-growth anneal-ing, in addition to the crystalline improvement revealed by XRD results. Fig. 4(b) and (d) are the KFM images of the n- and p-type ZnO epi-layers, respectively. No apparent correlation between the topography and KFM images was observed in both cases. This ruled out the possibility that KFM contrast was originated from the topographic features. It is noteworthy that the signs of
Fig. 3 (a) LT PL spectra of the as-deposited and annealed samples. (b) Temperature-dependent PL spectra of the annealed ZnO layer in NBE region.
Fig. 4 AFM topography (5 5 mm) of (a) the n-type as-deposited ZnO layer, and (c) p-type ZnO layer after annealing at 600C. The corre-sponding KFM images simultaneously recorded with (a) and (c) are shown on (b) and (d), respectively.
VSare different in the two samples. VSof the p-type ZnO layer
was positive, within the range of 0.214 0.110 V, depending on the probed location. However, for the n-type ZnO layer, its VSis
negative, with a value within 0.340 0.110 V. This result signies the as-deposited n-type ZnO layer has a work function smaller than that of Pt but the work function of the annealed p-type ZnO layer is larger than that of Pt. This indicates that the observed change of the work function upon annealing reected the conversion of carrier type induced by dopant ionization.
To further examine the change of VSwith sample
conduc-tivity type, we also preformed EFM measurements. EFM probes the amplitude of the electrostatic force on the tip, Fu, with the
sample bias voltage Vsampleas a parameter. Typically, the
spec-trum of Fuas a function of Vsampleat any given position on the
sample exhibits a V-shape prole, as shown in Fig. 5, and the value of Vsampleassociated with the minimum in Fuequals to
the VSat that position.17,18Fig. 5(a) and (b) illustrate the local
spectra of Fu recorded at two specic locations, which show
distinct contrast in the corresponding KFM images shown in the up-right corners, on the as-deposited and annealed samples, respectively. In the spectra taken at points A and B on the n-ZnO layer, Fu reached the minimum at the same value Vsample 0.394 V, implying that both points had the same VS
value and the work function of the n-type ZnO is lower than that of Pt. In contrast, the values of Vsamplewith minimal Fuat points
C and D in p-type ZnO layer are signicantly different, 0.151 and 0.308 V, respectively, revealing the nonuniformity in VS
distri-bution, which may be attributed to the inhomogeneous diffu-sion of As caused by structural defects, e.g. vacancies, dislocations, grain boundaries, etc. Furthermore, the positive Vsampleto nullify Fuof the annealed sample manifests that the
p-type ZnO layer has a larger work function than that of Pt. According to the VSdeduced from KFM and EFM results and
given electrical affinity of ZnO, cZnO ¼ 4.2 eV,25 the band
diagrams of both n- and p-type ZnO layers were constructed, as depicted in the insets of Fig. 5. At the surface of the n-type ZnO layer where VS is 0.394 V, its Fermi level (EF) is located at
1.06 eV below conduction-band minimum (CBM) at the surface; for the p-type ZnO, taking VS¼ 0.23 0.078 V from the EFM
results, EFat the surface is located at 1.68 0.079 eV below
CBM, or equivalently 1.69 0.079 eV above valence-band maximum (VBM) with Eg¼ 3.37 eV adopted as the ZnO band
gap at RT.
It is noted that the EFdifference between n- and p-type ZnO
epi-layers, 0.589–0.75 eV, is much smaller than ZnO band gap 3.37 eV, implying the existence of surface states near the mid gap. These surface states would induce band bending at the band edges and consequently Fermi-level pinning. Similar results have been reported by Allen et al.14who found that EFof
n-type ZnO was pinned in the band gap due to interface states caused by structural defects.
To estimate the density of surface states of the n- and p-type ZnO epi-layers, a uniform charge model in the depletion region was applied.26According to the model, surface charge density is
expressed ass ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffij2eND303rV0j p
, where ND(NAfor p-type ZnO)
denotes the doping density coming from the ionized donors in the depletion region,3r¼ 7.77 is the relative dielectric constant
of ZnO,27and the band-bending voltage V0can be written by eV0
¼ FPt cZnO eVS (EC EF). For the n-type ZnO layer, its EFis
suggested to lie in the conduction band, i.e. EF EC, because
the electron concentration n¼ 5.78 1018 cm3determined
from the Hall effect measurements is larger than the ZnO effective conduction band density of states calculated from NC¼ 2 2pm* ekT h2 3=2
z 2:72 1018cm3, where k is the Boltz-mann constant, T is temperature, h is the Planck constant, and m*e ¼ 0.24m0 denotes electron effective mass.28 V0 is thus
determined to be 1.06 V. Furthermore, NDis approximated by
the electron density determined from the Hall measurements 5.78 1018cm3, as N
D[ NA. The surface charge density of
n-type ZnO layer is then calculated to bes 7 1012e cm2. Similar calculation was also carried out for the p-type ZnO layer. In order to calculate surface state density, we need to
Fig. 5 (a) The local electrostatic force Fu vs. Vsamplecurves of the n-type ZnO layer recorded at points A and B, marked on the KFM image depicted in the inset shown in the upper right corner. Similar spectra of the annealed p-type ZnO layer taken at points C and D are shown in (b). The schematic band diagrams of the n- and p-type ZnO layers are shown as the insets in the respectivefigures.
determinate the concentration of acceptors, NA, which can be expressed as29 pðp þ NDÞ NA ND p¼ NV g exp EkTA z p2 NA 1 p NA ; as NA[ND
where the acceptor activation energy EA, 127 meV and hole
concentration p, 7.6 1018 cm3 were obtained from our PL and Hall results, respectively, ND is the concentration of
compensating donors, g denotes acceptor degeneracy and is assumed to be 4, NV¼ 2 2pm* hkT h2 3=2 z 1:134 1019cm3 is the effective valence band density of states, where m*
hz m0is
hole effective mass.3With the numbers given above, we obtained
NA z 1.24 1021 cm3. Following EF EV¼ kT ln NV NA , we obtained EF EVdue to the negative kT ln
NV NA
value. With the average value of VS, 0.23 V, the average V0of the p-type ZnO layer
obtained from EFM is about1.69 V; the surface charge density of the p-type ZnO layer is thus1.3 1014e cm2.
These results revealed the shi of EF between the n- and
p-type ZnO layers was caused by the development of the depletion charge varying from7 1012to 1.3 1014e cm2; the corresponding state density was2.2 1014cm2eV1.30 Bard et al.31reported that a surface state density as low as1 1012cm2was sufficient to result in band bending and Fermi level pinning. In n- and p-type GaN epi-layers, Barbet et al.26 showed that the existence of a surface state density of a few 1013 states cm2eV1near the mid gap caused EFpinning and band
bending. In that case, EFof n-type GaN was found 1.34 eV below
CBM and p-type GaN's was 1.59 eV above VBM. Therefore, the observed small EF difference between the n- and p-type ZnO
epitaxial layers implies Fermi level pinning at the surface of the n- and p-type ZnO epitaxial layers caused by the existence of high density of surface states close to the ZnO mid-gap. Because the work function of chosen standard Pt 5.65 eV is close to the ZnO mid gap 5.89 eV, which is calculated bycZnO+ 0.5 Eg, even
though the Fermi levels of both n- and p-type ZnO are pinned near the mid gap and their difference is small, the work func-tion of the ZnO layer changed across that of Pt upon annealing.
Conclusions
Wurtzite ZnO epitaxial layers were grown on n-type cubic GaAs (001) substrates by pulsed laser deposition (PLD). The epitaxial relationship between the ZnO layers and GaAs follows (0001)h1010iZnOk(001)h110iGaAsas determined by X-ray
diffraction (XRD). Post-growth annealing of the as-deposited n-type ZnO epitaxial layer lead to carrier type switching from electron to hole, which was attributed to the arsenic diffusion from the substrate. The surface electrical properties of the ZnO layers characterized by KFM and EFM revealed the exis-tence of high surface state density of a few 1014 cm2 eV1 close to the ZnO mid-gap. Fermi level are found at 1.014 eV below CBM and 1.612–1.769 eV above VBM for n- and p-type
ZnO layers, respectively. As compared with the hole concen-tration of ZnO doped with other group-V elements, e.g. N,3our result seems to be high. However, surface effects are known to particularly important in affecting the electrical properties of p-type ZnO, e.g. surface conductivity or the development of depletion layer caused by chemical adsorption.32,33 Surface
conduction effect, mixed conduction, or photoconduction are possible causes of the obtained low Hall voltage and conse-quently the high hole concentration. In this study, it is demonstrated that the existence of surface states indeed has a great inuence on the electrical properties of ZnO lms.
Acknowledgements
The National Science Council (NSC) of Taiwan supported this work under Contracts NSC 102-2112-M-213-004-MY3, NSC 100-2112-M-213-002-MY3, and NSC 102-2112-M-009-016-MY3.
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