Thickness-dependent lattice relaxation and the associated optical properties of ZnO epitaxial films grown on Si (111)

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Thickness-dependent lattice relaxation and the associated optical properties

of ZnO epitaxial films grown on Si (111)

W.-R. Liu,

a

B. H. Lin,

ba

C. C. Kuo,

b

W. C. Lee,

c

M. Hong,

d

J. Kwo,

ef

C.-H. Hsu*

ab

and W. F. Hsieh*

b Received 5th July 2012, Accepted 31st August 2012

DOI: 10.1039/c2ce26074c

The evolution of the strain state as a function of layer thickness of (0001) oriented ZnO epitaxial films grown by pulsed-laser deposition on Si (111) substrates with a thin oxide Y2O3buffer layer was

investigated by high resolution X-ray diffraction (XRD). The ZnO layers experience a tensile strain, which gradually diminishes with increasing layer thickness. Regions with a nearly strain-free lattice develop as the layer thickness exceeds a critical value and are correlated with the emergence of the ,112¯0. oriented crack channels. The influence of the biaxial strain to the vibrational and optical properties of the ZnO layers were also studied by micro-Raman, optical reflectance, and

photoluminescence. The deformation-potential parameters, aland bl, of the E2(high) phonon mode

are determined to be 2740.8 ¡ 8.4 and 2818.5 ¡ 14.8 cm21, respectively. The excitonic transitions associated with the FXA, FXB, and DuXAemissions and the A-exciton binding energy all show linear

dependence on the in-plane strain with a negative slope.

Introduction

ZnO, a II–VI compound semiconductor, is a promising material for high efficiency light-emitting devices and optical applications for UV luminescence because of its wide direct band gap, 3.37 eV, and large exciton binding energy, 60 meV near 295 K.1

Because of low cost, excellent quality, large-area availability of Si wafer, and, most importantly, the unique opportunity of integrating well-established Si electronics with ZnO-based optoelectronic devices, many efforts has been involved in growth of high-quality ZnO on Si. Unfortunately, direct growth of epitaxial ZnO films on Si is difficult due to large diversity in lattice constants (15.4%) and thermal expansion coefficient (56%) as well as the formation of amorphous SiO2 at the

ZnO–Si interface.2 Much effort has therefore been devoted to grow ZnO epitaxial films with the aid of a buffer layer of various materials, such as c-Al2O3, Y2O3, Lu2O3, Sc2O3 and Gd2O3

(Ga2O3).3–7 Y2O3 has attracted great attention because of its

high dielectric constant, high conduction band offset, and

thermodynamic stability with Si and is a promising candidate as an alternative gate dielectrics.8–10The formation enthalpy of Y2O3is larger in magnitude than that of SiO2and ZnO (DHY2O3

= 21905.31 kJ mol21, DHSiO2 = 2910.7 kJ mol

21

, and DHZnO=

2350.5 kJ mol21).11,12This implies the formation of an amorphous

silica layer at the Y2O3–Si interface can be obstructed and provides a

nice template for subsequent epitaxial growth. Previous studies showed that ZnO epitaxial films with high crystalline quality can indeed be grown on Si by using a thin Y2O3buffer layer. The lattice

of the as-obtained ZnO aligns with the hexagonal O sub-lattice in Y2O3and the interfacial structure can be well described by domain

matching epitaxy with 7 or 8 ZnO {112¯0} planes matching 6 or 7 {44¯0} planes of Y2O3, leading to a significant reduction of residual

strain.3The residual strain built up in an epi-film, induced by the lattice and thermal mismatches between the overlayer and the substrate, is known to cause a significant modification in its valence-band configuration. Hence, careful characterization of the strain state of a ZnO epi-film is pivotal for understanding the influence of strain on its electronic and optical properties and paving the way for the future application of ZnO in photoelectronic devices.

Even though many works reported the strain effects on the electronic and optical properties of ZnO epi-layers grown on (0001) oriented sapphire, on which ZnO is compressively stressed,13 much less is known about the influence on the lattice-dynamical, structural, optical and vibrational properties of the ZnO epi-layers on Si, where ZnO is under a tensile strain. In this work, the strain state of the tensile-stressed ZnO epi-films was systematically varied as a function of layer thickness in the studied range, 24–1200 nm, and measured by X-ray diffraction. The optical properties of the ZnO films were characterized by optical reflectivity (OR) measurements, photoluminescence at

aDivision of Scientific Research, National Synchrotron Radiation Research

Center, Hsinchu 30076, Taiwan E-mail: chsu@nsrrc.org.tw; Fax: +886-3-578-3813; Tel: +886-3-578-0281/7118

bDepartment of Photonics and Institute of Electro-Optical Engineering

National Chiao Tung University, Hsinchu 30010, Taiwan E-mail: wfhsieh@mail.nctu.edu.tw; Fax: +886-3-571-6631; Tel: +886-3-571-2121/56316

cDepartment of Materials Science & Engineering, National Tsing Hua

University, Hsinchu 30013, Taiwan

dGraduate Institute of Applied Physics and Department of Physics,

National Taiwan University, Taipei 10617, Taiwan

e

Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan

f

Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan

Cite this: CrystEngComm, 2012, 14, 8103–8109

www.rsc.org/crystengcomm

PAPER

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low temperature (LT) and micro-Raman spectroscopy accord-ingly. The phonon deformation-potential parameters, which are linear coefficients describing the phonon frequency shift with residual strain, are also determined.

Experiments

Si (111) wafers were cleaned by the Radio Corporation of America (RCA) method and hydrogen passivated by a buffered hydrofluoric HF acid solution before being put into a multi-chamber MBE/electron-beam evaporation UHV system.8A thin Y2O3film was then deposited using electron beam evaporation

from a high-purity Y2O3source, with a cubic bixbyite structure

of lattice constant a = 10.606 A˚ , on the Si surface, with substrate temperatures maintaining at about 770uC. The details of the growth conditions and the structure of the Y2O3 layer were

reported elsewhere.9,14The Y2O3–Si composite substrates were

then transferred in air to a pulsed laser deposition (PLD) growth system. Prior ZnO deposition, Y2O3–Si (111) substrates were

thermally treated aty375 uC under UHV conditions to clean the surface and to remove the moisture. A beam from a KrF excimer laser (l = 248 nm) at a repetition rate of 10 Hz was focused to produce an energy densityy5–7 J cm22

on a commercial hot-pressed stoichiometric ZnO (5N) target. Substrate temperature was increased to 400uC for the successive growth of ZnO layers on the composite substrates without oxygen flow; the growth rate isy0.96 A˚ s21.15

XRD measurements were performed with a four-circle diffractometer at beamline BL13A of the National Synchrotron Radiation Research Center, Taiwan, with incident wavelength 1.0238 A˚ . Two pairs of slits located between the sample and the detector yielded a typical resolution of better than 4 6 1023A˚21. The samples were also characterized by spatially-resolved Raman scattering using the 488 nm line of an argon ion laser at room temperature (RT). The spot size of the focused laser beam is approximately 1 mm. The scattered light was dispersed by a SPEX 1877C triple spectrograph equipped with a liquid nitrogen-cooled charge-coupled device at 140 K. PL measurements were carried out using a He–Cd laser with a wavelength of 325 nm as the pumping source; a broadband light source (Spex 1682) was utilized for optical reflection (OR) measurements at 13 K. The emitted light was dispersed by a Triax-320 spectrometer and detected by an UV-sensitive photomultiplier tube. The thickness of the thin ZnO films was derived from the period of the Kiessig fringes in X-ray reflectivity curves. For the thick films, the thickness was acquired from the period of interference fringes in room temperature PL spectra and scanning electron microscopy (SEM) cross sectional images.

Results and discussion

Fig. 1 illustrates the XRD h–2h radial scan along the surface normal of a 24.6 nm thick sample. The pronounced peaks centered at 2.003 and 2.428 A˚21 are Si 111 and ZnO 0002

reflections, respectively; the shoulder at 2.06 A˚21is attributed to Y2O3222 Bragg peak. The presence of the pronounced Kiessig

fringes around ZnO 0002 and Y2O3 222 reflections reveals the

good crystalline quality of the deposited layers and the sharp interfaces between ZnO–Y2O3 and Y2O3–Si. Two different

thicknesses, 24.6 and 9.75 nm, were derived from the fringe periods, which correspond to the ZnO and Y2O3 layer,

respectively. These numbers are in agreement with the values obtained from X-ray reflectivity. Moreover, the peak width of the ZnO 0002 reflection, 0.02618 A˚21, yields a vertical coherence

length of 23.9 nm. This value is close to the ZnO layer thickness, indicating that its structure remains coherent over almost the entire thickness. The intensity profile of the azimuthal w scans across ZnO 101¯1, Y2O3440, and Si 220 off-normal reflections

are depicted in Fig. 2. Six evenly spaced ZnO 101¯1 peaks with their angular positions coinciding with that of the Y2O3 440

peaks verify that the hexagonal ZnO film is epitaxially grown on the Y2O3–Si (111) substrate. The observation of two sets of Y2O3

440 reflections offset by 60u in azimuth are ascribed to the coexistence of two rotational variances of the Y2O3buffer layer.

The angular position of the stronger set is rotated with respect to that of the Si 220 by 60u, demonstrating that the Y2O3on Si is

predominantly of B-type orientation, i.e., Y2O3{440} || Si {1¯1¯2}.

The result reveals the relative orientation of the layers follows (0001)v2110wZnOjj(111)v101wY2O3jj(111)v101wSi.

3By fitting Fig. 1 XRD radial scan along the surface normal of a 24.6 nm thick ZnO layer grown on the Y2O3–Si (111) composite substrate.

Fig. 2 XRD w scans across ZnO 101¯1 and Si 220 off-normal reflections of a 24.6 nm thick ZnO layer.

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the angular positions of many Bragg reflections, we determined the lattice parameters of the ZnO layer to be a = 3.269 A˚ and c = 5.176 A˚ . As compared with the bulk values, a = 3.249 A˚ and c = 5.206 A˚ determined from a ZnO wafer, the ZnO epitaxial film was tensily strained (0.64%) in the lateral direction and the lattice along the growth direction is correspondingly compressed by 0.56%.

To probe the strain variation as a function of layer thickness, XRD radial scans along surface normal and [101¯0] lateral direction were performed on samples of ZnO thickness varying from 24.6 to 1200.5 nm. Fig. 3a and b illustrate, respectively, the profile of the ZnO 0006 normal reflection and 303¯0 in-plane reflection. With increasing layer thickness, the center of ZnO 0006 reflection progressively shifts toward smaller normal scattering vector, qz, and approaches the bulk value, marked

by the dashed line in Fig. 3a, indicating the increase of the c-axis lattice constant. Meanwhile, the center of ZnO 303¯0 surface reflection exhibits an opposite trend, i.e., increasing with larger thickness, which reveals the relaxation of the tensile strain as the film grows thicker. Besides the relaxation of the homogeneous strain, the peak width of both reflections becomes narrower with increasing thickness, implying the reduction of inhomogeneous strain which is possibly accompanied by increasing structural coherence length. It is noteworthy that an extra peak appears in the radial scans across the 303¯0 reflection for samples with ZnO layer thickness of 555.2 nm and above. The circles in Fig. 4a depict the ZnO 303¯0 peak profiles of the 555.2 nm thick ZnO layer, which can be nicely decomposed into two Gaussian functions, displayed by dashed curves. The emergence of the extra peak SRlocated at a larger lateral scattering vector q||=

6.69924 A˚21, corresponding to a small tensile strain exx =

20.0011%, than that of the original one SS located at

6.67215 A˚21(exx= 0.397%) reveals the development of regions

with a nearly fully relaxed lattice as the film thickness exceeds a

critical value. Carefully examine the peak profile of the specular (0006) reflection of the same sample, shown in Fig. 4b, we observed an asymmetric shape skewing toward the low qzside.

The peak can also be fitted by two Gaussian functions, reflecting the change of the vertical lattice constant in correspondence to the relaxation of lateral lattice constant. The intense one, NS,

centered at high qzside 7.26885 A˚21is associated with peak SSin

the 303¯0 reflection; they are originated from the stressed regions. Alternatively, the weak one, NR, centered at qz = 7.26356 A˚21

with larger vertical lattice constant is associated with peak SR

with smaller lateral lattice constant and they stem from the relaxed regions. As a function of layer thickness, the lateral and normal lattice constants, a and c, of the stressed regions determined by fitting the angular positions of several XRD Bragg reflections, are plotted in Fig. 5a. The lateral/normal lattice constant rapidly decreases/increases with layer thickness in the initial 200 nm and then progressively approaches the bulk value. The corresponding homogeneous strain along the in-plane and surface normal directions, exx~

a{a0 a0 and ezz~ c{c0 c0 , where a0 and c0denote the lattice constants of bulk ZnO in the relaxed

state, are depicted in Fig. 5b.

The optical microscopy image of the 345.6 nm thick ZnO layer is shown in Fig. 6a, where no crack is found. In contrast, a large density of crack channels running along the ZnO ,112¯0. directions with the {101¯0} side surface are well resolved in the surface image of the 555.2 nm thick ZnO epi-layers, shown in Fig. 6b. Apparently, the formation of the crack channels leads to the local relaxation of the tensile strain and accounts for the appearance of extra X-ray diffraction peaks SRand NRobserved

in the thick films. The preferred cracking direction reflects the anisotropic fracture toughness of ZnO. Ding et al. reported that the {101¯0} surfaces of wurtzite ZnO had the lowest surface

Fig. 3 XRD radial scans across ZnO (a) surface normal 0006 and (b) in-plane 303¯0 reflections of six samples with various layer thickness, d. The dashed lines mark the corresponding peak positions of bulk ZnO and the thick dashed curves are plotted to guide the eye.

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energy by simple bonding density calculation.16 The

develop-ment of the cracks is due to the tensile stress induced by post-growth cooling as a result of the mismatch in the thermal expansion coefficients aabetween ZnO 6.5 6 1026K21and Si

2.6 6 1026 K21.3 Even though Y

2O3 has a larger thermal

expansion coefficient 8.1 6 1026 K21 than ZnO, it cannot overcome the dictating lattice contraction originating form the Si substrate due to its small thickness.

The crystalline structure of wurtzite ZnO belongs to space group C4

6v(P63mc) and has the following optical phonon modes

A1+ 2B1+ E1+ 2E2at the Brillouin zone-center. Among them,

the E2 (high) mode is most sensitive to the strain and often

adapted for strain determination.17 Fig. 7 illustrates the room temperature micro-Raman spectra of the 555.2 nm thick sample recorded in the z(…)z geometry as shown by the schematic inset, where z is parallel to the ZnO c-axis. The spectra were taken with the laser beam focused at three spots with different distances from the cracks as displayed in the inset. Also plotted is the spectrum of a ZnO wafer as a comparison. The residual strain at

Fig. 4 (a) Peak profile of the in-plane 303¯0 reflection measured with incident angle aiequal to the critical angle for total external reflection, ac.

The profile is fitted by two Gaussian functions as noted by SSand SR. (b)

Peak profile of a XRD radial scan across the ZnO 0006 reflection along surface normal, which is fitted by two Gaussian functions as noted by NR

and NS. All the data were collected from the sample with a 555.2 nm

thick ZnO layer. Vertical dashed lines mark the location of correspond-ing Bragg reflections of a bulk ZnO. The numbers indicated are the corresponding FWHMs.

Fig. 5 (a) Lattice constants a and c of the ZnO films as a function of film thickness. The corresponding bulk values are depicted by dashed lines. (b) The homogeneous strain exx(in-plane) and ezz(surface normal)

of the ZnO films as a function of the film thickness. The positive values represent the tensile strain. The dashed curves are plotted to guide the eye.

Fig. 6 Optical images of the (a) 345.6 nm and (b) 555.2 nm thick ZnO films grown on Y2O3–Si(111) composite substrate.

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each location is reflected by the corresponding amount of red shift of the E2(high) phonon frequency with respect to that of a

strain-free ZnO wafer, 437.78 cm21. The energy of the E2(high) mode

measured right on the crack channel, location A, coincides with that of the ZnO wafer, confirming that the local lattice is fully relaxed by the development of the cracks. Moving away from the cracks, the tensile strain gradually builds up as manifested by the increasing red shift observed in locations B and C. Further moving away from the cracks does not cause further red shift of the E2(high) frequency.

The interior of the regions encircled by the cracking channel are tensily strained and give rise to the XRD peaks SSand NSin Fig. 4.

Alternatively, the Srand Nrpeaks are associated with the relaxed

regions in the immediate vicinity of the cracks.

To quantitatively characterize the influences of stress on optical phonons, the frequency shift of the E2(high) mode, Dvl,

was analyzed as a function of lateral strain, exx. The

micro-Raman spectra, illustrated in Fig. 8a, were recorded in the center of the stressed regions, which is at least 15 mm away from the nearby crack channels,18and the E2(high) phonon frequency is

determined by fitting the Raman peak by a Lorentzian line shape. The strain is deduced from the XRD data and the center of the SSpeak, corresponding to the stressed regions, is adopted.

The E2(high) phonon mode frequency shift vs. the lateral strain

of the ZnO grown on Si with a Y2O3 buffer layer (downward

triangles) is plotted in Fig. 8b. In addition, the data from the ZnO layers grown under the similar conditions on Si with a nanometer-thick Gd2O3(Ga2O3), GGO, buffer layer (squares)7

and on c-plane sapphire (upward triangles), where the ZnO layers are, respectively, under a tensile and compressive strain, are also plotted. In all three systems, the frequency shift exhibits a monotonic dependence on the strain. From the linear least-squares fit to all the data, ranging from compressive to tensile strain, we obtained a slope m = 2665.53 ¡ 31.5 cm21.

The change in frequency of a phonon mode l can be described in terms of the phonon deformation potential constants and strain components. Under symmetry conserving stress and in the

linear approximation, the frequency shift Dvlof a crystal with

C4

6v(P63mc) space group symmetry can be expressed by

Dvl= 2alexx+ blezz (1)

, where the deformation potential constants aland bldenote the

frequency change of phonon per unit strain along lateral and c-axis directions, respectively.19,20 This equation holds for the cases of hydrostatic pressure and biaxial strain; where the latter is often caused by lattice mismatch or thermal strain during epitaxial growth.17 Based on elasticity theory, the strain along

the surface normal is proportional to the lateral strain with the ratio Rb= (ezz/exx)b= 22C13/C33under the biaxial strain, where

Cij denotes the ij component of the elastic stiffness tensor of

ZnO.21,22Eqn (1) can thus be rewritten as Dvl~2(al{bl

C13 C33

)exx (2)

The averaged experimental value of Rb = 20.92 is reasonably close to the calculated value 21.00 by adopting C13= 105.1 and

C33 = 210.9 GPa reported by T. B. Bateman, indicating the Fig. 7 RT micro-Raman spectra recorded from the 555.2 nm thick ZnO

film in the z(…)z geometry, as illustrated by the schematic inset. The inset on the upper right corner shows the optical image of the sample surface with the positions of Raman measurements marked.

Fig. 8 (a) RT micro-Raman spectra measured in the stressed regions of the ZnO films of different thickness. (b) Frequency shift Dvlof the

high-energy E2phonon mode as a function of lateral strain exx. The straight

dashed line shows the best linear fit.

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validity of elasticity theory in the current case.23 The phonon frequency shift thus varies linearly with the lateral strain. To calculate these deformation potential constants, one more equation is required. The phonon frequency shift under hydrostatic compression and symmetry conserving condition is characterized by the bulk Gru¨neisen parameter c, which can be expressed by the deformation potential parameters aland bl, the

phonon frequency vl under strain-free conditions, and the

elastic stiffness constants of ZnO crystal as

c~{2(C33{C13)alz(C11zC12{2C13)bl vl(C11zC12z2C33{4C13)

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By inserting the average value for the Gru¨neisen parameter c =1.757,13,24the E2(high) phonon frequency vl= 437.78 cm21,

the elastic stiffness constants at 25uC, C11= 209.7, C12= 121.1,

C13= 105.1, and C33= 210.9 GPa, 23

all with the estimated error of 0.1–0.15%, into eqn (2) and (3), we solve the phonon-deformation potential constants for the E2(high) phonon mode

to be al = 2740.8 ¡ 8.4 and bl = 2818.5 ¡ 14.8 cm21,

respectively. These values are in good agreement with the results al = 2690 ¡ 110 and bl = 2940 ¡ 260 cm

21

reported by Gruber et al.13The discrepancy between the results could be due

to the uncertainties in the ZnO Gru¨neisen parameter and elastic constants used. The defects and unintentional impurity doping may also cause the difference.

The state at the conduction band minimum of ZnO is predominantly s-like (C7C). Under the action of crystal-field

and spin-orbit interaction, the p-like states in the valence band of wurtzite ZnO are split into 3 levels in the vicinity of the point. The 3 levels at the valence band maximum are commonly labeled as A, B, and C bands in the order of decreasing energy, as shown in the inset of Fig. 9a. Thomas25 and Hopfield26assigned the sequence of p-like valence band in the order of A-Cu

7V, B-C9V,

and C-Cl

7V due to the crystal field and negative spin-orbital splitting. On the contrary, Reynolds27 and Gil28 assigned the valence-band ordering as A-C9V, B-Cu7V, and C-Cl7V based on

polarized optical reflectance and magneto luminescence mea-surements on strain-free bulk ZnO crystals. Nevertheless, either ordering predicts that A and B transitions are allowed for light polarization E perpendicular to the c-axis (E)c), and the C transition is allowed for polarization E parallel to the c-axis (E||c). For many years, the assignment of valence band ordering is still debated and the influence of strain to the electronic structure is of great interest. To access the influence of biaxial strain on the exciton resonance energies of the ZnO epi-film, the optical reflectance (OR) and PL spectra were measured at low temperature. The resonant features in the OR spectrum of the 555.2 nm thick sample, shown in Fig. 9a, with transition energies equal to 3.373, 3.387, and 3.421 eV are attributed to the excitonic transitions associated with the A, B, and C bands, respectively. The B-free exciton (FXB) resonance band is well resolved in all

the samples with various thickness; its transition energy is depicted by the circles as a function of in-plane strain exx in

Fig. 9b. A PL spectrum of the 555.2 nm thick sample in the near-band-edge region is illustrated in Fig. 9a as well. The transitions associated with the A-exciton dominate the LT luminescence; among them the emissions at 3.3604 and 3.373 eV, ascribed to

the recombination of A-exciton bound to the neutral donors (DuXA) and the A-free exciton (FXA), respectively, are noted. By

fitting the temperature-dependent intensity variation of the FXA

line with the Arrhenius expression,29,30we obtained the binding

energy of A-exction 58.11 ¡ 2.4 meV, in good agreement with the 60 meV for bulk ZnO crystal. The transition energies of FXA,

DuXA, and the A-exciton binding energy derived from the PL

data are also depicted in Fig. 9b as a function of in-plane strain exx. The energies of FXA, FXB, and DuXA exhibit linear

dependence on exx and the corresponding slopes (dE/exx) are

23.739, 22.612, and 23.758, respectively. The difference of slopes of FXAand DuXAis about 19.3 meV, implying that the

binding energy of DuXAchanges at the rate of 19.3 meV with the

biaxial strain. According to Hayne’s rule, the binding energy of an exciton to a neutral donor–acceptor has a constant ratio to the binding energy of an electron–hole to the donor–acceptor.31–33 With the reported value 0.3 of Hayne’s constant a for ZnO, the variation of localization energy of the donor with strain is calculated to be approximately 64.3 meV.33–35The binding energy of the FXAalso exhibits a monotonic decrease with increasing

in-plane tensile strain, with a slope of 2294.1 meV. This diminishing trend is consistent with the result of the first-principles calculation based on density functional theory with a spatially non-local exchange and correlation functional and spin-orbit interaction.36 To compare our results with samples grown on different

Fig. 9 (a) Optical reflectance and PL spectra of the 555.2 nm thick ZnO epi-layer measured at 13 K. Inset illustrates the ZnO band diagram. (b) Transition energies of FXA, FXB, and DuXAof ZnO layers measured at

13 K and the binding energy of A exciton as a function of strain, exx.

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conditions, we calculate the strain-induced excitonic transition energy shift with respective to the strain along the c-axis (dE/ezz)

by taking into account the biaxial strain ratio Rb= 20.92 and the values associated with the A and B excitons are 4.06 and 2.84 eV, respectively. These numbers are within in the range withy2 eV for the ZnO grown on c-plane sapphire with and without a layer of GaN buffer layer13,37 and y15 eV for the ZnO grown on 6H–SiC.38The discrepancy may be attributed to the details of the micro-structure, such as defects, and also the difference in strain-free lattice constants adopted.

Summary

Thickness-dependent strain evolution of ZnO epitaxial films grown on Si(111) with a Y2O3buffer layer has been investigated. The ZnO

layers are tensily stressed, predominantly due to the difference in thermal expansion coefficient with Si. Drastic strain reduction occurs within the initial 200 nm, attributed to the large density of structural defects in the region near the ZnO–substrate interface as evidenced by the transmission electron microscopy images. Cracking channels develop as the layer thickness exceeds a critical value, less than 550 nm, and leads to the nearly fully relaxed lattice in the immediate vicinity. The interior of the regions encircled by the cracking channels retains a tensile strain ofy0.3%. Correlating the peak frequency of micro-Raman spectroscopy with the lattice constants determined by XRD, we found that the energy shift of the strain-sensitive E2(high) phonon mode varies linearly with the

in-plane biaxial strain. The phonon deformation-potential parameters of the E2(high) mode under a biaxial strain model are determined to

be al= 2740.8 ¡ 8.4 and bl= 2818.5 ¡ 14.8 cm 21

, respectively, in reasonably good agreement with what reported by Gruner et al.13

PL and OR results reveal that the energy of excitonic transitions of FXA, FXB, and DuXAalso exhibit a linear dependence on in-plane

strain. A-exciton binding energy also varies linearly with the in-plane tensile strain with a negative slope, which is consistent with theoretic prediction based on the first-principles calculation.

Acknowledgements

We thank Dr. Y. C. Lee of National Synchrotron Radiation Research Center, for his assistance in the micro-Raman measurements. National Science Council of Taiwan partly supported this work under grants NSC-100-2112-M-213-002-MY3 and NSC 100-2112-M-006-002-NSC-100-2112-M-213-002-MY3.

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數據

Fig. 2 XRD w scans across ZnO 101¯1 and Si 220 off-normal reflections of a 24.6 nm thick ZnO layer.
Fig. 2 XRD w scans across ZnO 101¯1 and Si 220 off-normal reflections of a 24.6 nm thick ZnO layer. p.2
Fig. 1 illustrates the XRD h–2h radial scan along the surface normal of a 24.6 nm thick sample
Fig. 1 illustrates the XRD h–2h radial scan along the surface normal of a 24.6 nm thick sample p.2
Fig. 3 XRD radial scans across ZnO (a) surface normal 0006 and (b) in-plane 303¯0 reflections of six samples with various layer thickness, d
Fig. 3 XRD radial scans across ZnO (a) surface normal 0006 and (b) in-plane 303¯0 reflections of six samples with various layer thickness, d p.3
Fig. 4 (a) Peak profile of the in-plane 303¯0 reflection measured with incident angle a i equal to the critical angle for total external reflection, a c .
Fig. 4 (a) Peak profile of the in-plane 303¯0 reflection measured with incident angle a i equal to the critical angle for total external reflection, a c . p.4
Fig. 6 Optical images of the (a) 345.6 nm and (b) 555.2 nm thick ZnO films grown on Y 2 O 3 –Si(111) composite substrate.
Fig. 6 Optical images of the (a) 345.6 nm and (b) 555.2 nm thick ZnO films grown on Y 2 O 3 –Si(111) composite substrate. p.4
Fig. 8 (a) RT micro-Raman spectra measured in the stressed regions of the ZnO films of different thickness
Fig. 8 (a) RT micro-Raman spectra measured in the stressed regions of the ZnO films of different thickness p.5
Fig. 9b. A PL spectrum of the 555.2 nm thick sample in the near- near-band-edge region is illustrated in Fig
Fig. 9b. A PL spectrum of the 555.2 nm thick sample in the near- near-band-edge region is illustrated in Fig p.6

參考文獻