Published: September 08, 2011
J. L. Shen
Department of Physics, Chung Yuan Christian University, Jhongli 32023, Taiwan
’ INTRODUCTION
An urgent and global need for renewable energy sources has aroused widespread research interest in potential photovoltaic materials. Such research efforts may pave the way to the gradual phasing out of conventional and nuclear power. Oxides are promis-ing owpromis-ing to their natural availability, environmental stability, and ecologically friendly characteristics.1 Moreover, because of its large electronegativity, oxygen forms chemical bonds with almost all elements to give the corresponding oxides. Zinc oxide (ZnO) is a wide-bandgap (∼3.4 eV at 300 K) semiconductor and crystallizes preferentially in the hexagonal wurtzite structure. By comparison with ZnSe and GaN, the relatively strong polar binding, deep excitonic level (∼60 meV), and biocompatibility with organic systems of ZnO make it highly attractive for use in functional optoelectronic devices.27Substitution of an increas-ing fraction of the Zn atoms by Mg can shift the band gap of Zn1xMgxO into the deep ultraviolet region.6,8Additionally, the
ionic radius of Mg2+(0.57 Å) closely matches to that of Zn2+ (0.60 Å), making this ternary alloy a suitable barrier material in ZnO-based heterostructures and solar-blind devices.26
The technological importance of Zn1xMgxO has motivated
detailed and fundamental studies as well as application-oriented research. Although the optical properties of Zn1xMgxO have
been extensively investigated, the effects of both Mg and pressure
on the lattice dynamics and crystalline properties of Zn1xMgxO
remain unexplored. Previous Raman studies of ZnO at ambient and high pressures have yielded somewhat unclear and contra-dictory results. (i) The assignments of the vibrational modes at 202.7 and 332.7 cm1are contentious.9,10Furthermore, origin of the phonon mode at 511.5 cm1, which appears only after intentional doping, is controversial.1113 (ii) Evidence of the pressure-dependent LO-TO splitting and transverse effective charge in ZnO is contradictory. Decremps et al. and Manjon et al. found that the LO-TO splitting and the transverse effective charge of the E1mode in ZnO increase upon compression.14,15
However, Reparaz et al. demonstrated that the LO-TO splitting and the transverse effective charge decrease with increasing pressure in both A1and E1modes.16(iii) Previous high-pressure
Raman measurements have shown that the wurtzite-to-rocksalt phase transition of ZnO completes at 8.39.0 GPa.14,15,17
These values are far below the experimental values (above 12.8 GPa) that were obtained using high-resolution angular dispersive X-ray diffraction (XRD).18Such a difference is probably caused by a
weak Raman signal, large pressure interval, and an undetected
Received: August 10, 2011 Revised: September 7, 2011 ABSTRACT:This investigation systematically studies the lattice
dynamics and crystalline properties in Zn1xMgxO using
high-pressure Raman spectroscopy. The incorporation of Mg and the application of external pressure cause distinct phonon vibrational behaviors in ZnO. Accordingly, the 202.7, 332.7, and 511.5 cm1 phonons, which have been controversially assigned, can be con-clusively identified. Detailed Raman spectra reveal that the metallic phase transition of ZnO is complete by around 13.2 GPa, which pressure is found to decrease as the Mg content increases. Upon
pressure release, an unusual hysteresis effect (>10.0 GPa) in Zn1xMgxO is observed. The degree of crystal ionicity and anisotropy
importantly affects the phase transition pressure of Zn1xMgxO. Under ambient conditions, ZnO becomes more ionic upon the
incorporation of Mg and becomes more covalent under higher pressure. These results are caused by the interplay between the pressure dependence of the high-frequency dielectric constant and Born’s transverse dynamical effective charge. The E1A1splitting of the
low-frequency (<100 cm1) E2 vibrational phonon. These
apparent inconsistencies strongly motivate this thorough study of high-pressure Raman phonon dynamics in Zn1xMgxO.
In this paper, Raman scattering of Zn1xMgxO (0 e x e
0.10) are investigated systematically as a function of Mg composition at ambient condition and under hydrostatic pressure. To study thoroughly the lattice dynamics and crystal-line stability of Zn1xMgxO, both upstroke and downstroke
high-pressure Raman measurements are carefully made. The origins of the vibrational modes at 202.7, 332.7, and 511.5 cm1 are determined from the high-pressure Raman results. Addi-tionally, the pressure-dependence of the transverse effective charge, crystal anisotropy, and pressure-induced metallic phase transition of Zn1xMgxO with various Mg contents are also
investigated.
’ EXPERIMENTAL SECTION
Zn1xMgxO (x = 0, 3.0, 7.0, and 10.0%) powders were
synthesized by the citric-acid-assisted solgel method as described elsewhere.19,20The wurtzite phase of the Zn1xMgxO powders at
ambient pressure was identified by XRD. The morphology of the powders was studied using scanning electron microscopy (SEM). The Mg content was determined by energy-dispersive X-ray (EDX) analysis. The deviations of Mg contents at various positions in the samples were 3.0 ( 0.3%, 7.0 ( 0.5%, and 10.0 ( 0.5%, as determined by EDX measurements. The photoluminescence19,20 and Raman spectra recorded at different positions throughout the samples were all identical.
High-pressure Raman measurements were all made at room temperature using a ruby-calibrated diamond anvil cell (DAC).21 A liquid methanolethanol 4:1 mixture was utilized as the pressure-transmitting medium, and the pressure gradient was less than 0.2 GPa throughout the sample chamber. The Raman spectra of the Zn1xMgxO and the ruby fluorescence were obtained in
back-scattering geometry using the 514.5-nm line of an Ar+-ion laser. Signals were dispersed using a Horiba iHR550 spectrometer with a 2400 gram/mm grating and detected using a multichannel LN2
-cooled charge-coupled device (CCD). The exact peak positions were determined by fitting each spectrum with a Lorentzian curve, and the reproducibility of all Raman peaks was better than(0.2 cm1.
’ RESULTS AND DISCUSSION
A. At Ambient Pressure.Figure 1 shows SEM images of the Zn1xMgxO (x = 0 and 10.0%) powders. The average crystalline
diameters (dsize) of ZnO and ZnMgO powders were around
300 and 500 nm, respectively. The Zn1xMgxO particle sizes
greatly exceeded the ZnO exciton Bohr radius (aB≈ 2.34 nm)22
and were close to the excitation wavelength (λexc) such that the
quantum confinement and size effects were negligible (aB, dsize
≈ λexc). Figure 2 shows Raman spectra of Zn1xMgxO under
ambient conditions with mode assignments of the observed peaks. The two intense peaks of E2low(98.8 cm1) and E2high
-(438.3 cm1) dominate the Raman spectrum of the ZnO. The peaks at 380.6 and 411.1 cm1are attributed to the A1(TO) and
E1(TO) phonons, respectively. A broad and asymmetric phonon
at around 580.0 cm1comprises two adjacent peaks of A1(LO)
and E1(LO) phonons at 574.4 and 584.0 cm1, respectively. The
phonon peaks at 485.0, 539.8, and 615.8 cm1 are attributed to the 2LA(M-K), 2LA(L,M,H), and TA+TO (H,M) modes, respectively. As shown in Figure 3, both E1and E2phonons are
associated with atomic motions in the ab plane, whereas the atomic motions of A1and B1phonons occur along the c axis. In
addition to the aforementioned phonons, three modes at 202.7, 332.7, and 511.5 cm1(x > 0) are also found. The origins of these phonons are controversial and will be discussed later. The observed Raman phonon frequencies of ZnO correlate well with previous works.9,10,14,16 In this study, the optical phonons are
Figure 2. Raman spectra of Zn1xMgxO (x = 0, 3.0, 7.0, and 10.0%) under ambient pressure.
Figure 3. Displacement vectors for six optical phonon modes in wurtzite ZnO.
observable at both the Stokes and the anti-Stokes sides of each Raman spectrum. Moreover, the phonon frequencies are inde-pendent of excitation wavelength (457.9, 488.0, and 514.5 nm). Unlike the higher oriented c axes of bulks and films on specific substrates, the crystal axes of powder are randomly tilted relative to the laser excitation polarization. Therefore, the peculiar crystal-line geometries of Zn1xMgxO powders lead to our observation
of all Raman-active phonon modes.
To gain insight into the lattice dynamics of Zn1xMgxO, parts
ac of Figure 4 show the highlighted zone-center Raman spectra. Table I presents the phonon frequency and the LO-TO splitting of each phonon. Clearly, as Mg is substituted into ZnO, the A1,
E1, and E2low [Figure 4b] phonons together with the acoustic
phonons shift to higher frequencies. However, the E2high[Figure 4c]
and 332.7 cm1phonons behave oppositely. These phonon shifts are accompanied by intensity quenching and line width broadening, which could be attributed to Mg-induced translational crystal asymmetry and alloy fluctuations. Additionally, as indicated in Table I, the LO-TO splittings of both A1and E1modes increase
with Mg content. The results imply that incorporating Mg makes ZnO more ionic. This behavior is consistent with the fact that the ionicity (fi; Phillips’ ionic scale) of MgO (0.841) exceeds that of
ZnO (0.616).23
Generally, the substitution of Mg for Zn atoms decreases the reduced mass of the oscillator, shifting the Raman phonons to higher frequencies. However, the E2highand 332.7 cm1phonons
shift to lower frequencies. This is because the E2highphonon
corre-sponds mainly to the vibrations of the oxygen (lighter) atoms,24so the difference between atomic masses, mMg(24) < mZn(65), cannot
be responsible for the decrease of the E2highphonon frequency. As
previously demonstrated, the lattice constant a of Zn1xMgxO
increases monotonically with x.25Therefore, the lattice expansion in the ab plane accounts for the E2highphonon softening (Figure 3). A
similar result is obtained for the 332.7 cm1phonon, which has been previously attributed to either the transverse acoustic overtone at the K-M-∑ point or the difference between E2highand E2lowin ZnO.9,10As x
is increased, the phonon frequency correlates closely with the dif-ference between E2highand E2low. Moreover, the phonon shift agrees
well with the opposite vibrational behaviors of E2low and E2high
phonons. These experimental results indicate that the E2high- E2low
complex phonon is most likely the origin of the 332.7 cm1mode.
Such an assignment will be further verified by making measurements under high pressure.
In addition to the host Raman phonons of ZnO, a vibrational mode at 511.5 cm1(D hereafter) is clearly observed when Mg is intentionally incorporated. Interestingly, increasing the Mg con-tent slightly increases the intensity of the D mode but its frequency is unaffected. The origin of this phonon is still under debate. Kaschner et al. observed this additional phonon in N-doped ZnOfilms and interpreted the occurrence as an N-related local vibrational mode.11 However, Bundesmann et al. detected the phonon in ZnOfilms that were doped with Fe, Sb, and Al, and intentionally grown without N incorporation.12 Because of the large variation in the masses of these dopants, they suggested that the intrinsic host lattice defects were responsible for this phonon. Manjon et al. attributed this phonon in N-doped ZnO films to the disorder-activated 2B1lowmode due to the relaxation of Raman
selection rules that is induced by the breakdown of the crystal symmetry.13
In the case considered herein, the D mode cannot be ascribed to the N-related phonon because the Zn1xMgxO powders were
all grown without additional N-doping. Also, the D mode cannot be an activated silent B1lowmode because (i) B1-related phonons
have not been observed in Zn1xMgxO even under high-pressure
conditions (high crystal asymmetry) and (ii) the D mode behaves entirely differently from B1low, which should shift toward
higher frequencies as x increases (Figure 3). On the basis of these observations, a structure or a complex defect with a crystal symmetry that differs from that of the host lattice accounts for the D mode in Zn1xMgxO (x > 0). Therefore, results of this
study suggest that the complex defects of Zn and O interstitials (ZnI-OI), which are induced by incorporating Mg, are the origin
of the D mode. Zinc (oxygen) vacancies and antisites can be ruled out since they degrade the entire crystal isotropy without providing related phonon modes.26 Further evidence for the ZnI-OIcomplexes under high pressure will be discussed later.
B. Under High Pressure. Figure 5a shows the pressure-dependent Raman spectra of ZnO recorded with increasing pressure up to 20.0 GPa. Figure 5b plots the pressure depen-dence of the phonon frequencies, to which straight lines can be fitted (Table II). As external pressure is applied, the reduction in lattice constants should shift all Raman phonons toward higher frequencies. However, two remarkable exceptions—the E2
low
and
Figure 4. Highlighted zone-center Raman spectra of (a) A1, E1, D, and 332.7 cm1phonons, including Lorentzianfits for LO modes, and (b) E2lowand (c) E2highphonons of Zn1xMgxO under ambient pressure. Dashed lines and solid circles are guides for the eyes.
phonon splitting phonon frequencyΔω (cm1) A1(LO) A1(TO) 193.8 195.5 200.1 201.7 E1(LO) E1(TO) 172.9 177.3 184.3 187.3
the 202.7 cm1phonons—are observed in Figure 5a. The soft-ening of the E2lowphonons with increasing pressure is observed in
all of the Zn1xMgxO samples discussed herein. A similar
experimental result was obtained for wurtzite GaN.27The nega-tive pressure coefficient of the E2lowphonon in ZnO and GaN can
be attributed to the soft pressure-dependent C66elastic constant;
however, the hard C66elastic constants in wurtzite AlN and SiC
result in the positive pressure coefficients of the E2lowphonons.28
The phonon at 202.7 cm1in ZnO has been previously assigned to 2E2lowor 2TA.9,10In this study, although incorporating Mg and
applying external pressure cause opposite phonon behavior of the E2low phonon, the frequency shift of the 202.7 cm1 phonon
closely corresponds to that of the E2 low
phonon. These results suggest that the E2lowphonon should contribute significantly to the
202.7 cm1phonon and, therefore, the 202.7 cm1phonon can be assigned to the 2E2low. The assignment will be further
con-firmed under high-pressure measurements.
In Figure 5a, the pressure-induced phonon shifts are accom-panied by significant falls in phonon intensities. As the pressure is increased to 9.6 GPa, three additional phonons with similar intensities simultaneously appear at around 150, 550, and 590 cm1, and the latter two peaks overlap as a broad vibrational band in the range between 500 and 650 cm1. Above 9.6 GPa, all A1 and E1
phonons gradually vanish, and the Raman spectra are dominated by the three additional phonons. As the pressure further increases to 13.2 GPa, the two intense E2low and E2high phonons in the
wurtzite structure completely disappear, and the sample darkens. These phenomena are strong evidence of a pressure-induced metallic phase transition.21,29,30In fact, the first-order Raman phonon modes are forbidden by the selection rules in rocksalt structures. Thus, the metallic phase transition should be accom-panied by the wurtzite-to-rocksalt phase change as previously described.14,15,17 The wurtzite-to-rocksalt phase transition of ZnO is complete by around 13.2 GPa, as determined using detailed high-pressure Raman measurements, which finding agrees closely with the high-pressure XRD results obtained by Mao’s group.18
A close inspection of the three additional modes in Figure 5a indicates that these phonons emerge at around 9.6 GPa and become more intense with increasing pressure until the wurtzite-to-rocksalt
phase transition is complete. Obviously, these phonons are, in contrast with the first-order Raman phonons in the wurtzite phase, insensitive to pressure. In the rocksalt phase, these addi-tional phonons are still observable and slightly shift to higher frequencies with increasing pressure. On the basis of these findings, these additional Raman phonons that appeared at high pressures are vibrational modes of rocksalt ZnO. The compli-cated Raman signals in the pressure range between 9.6 and 13.2 GPa reflect the coexistence of wurtzite and the rocksalt phase, revealing that the ZnO undergoes a gradual phase transformation from wurtzite to rocksalt.
Figure 6a show the upstroke pressure-dependent Raman spectra of Zn0.90Mg0.10O. Several interesting conclusions can
be drawn from a comparison with those of ZnO. (i) In addition to the A1, E1, and E2phonons, the D mode, whose frequency is
unaffected by the Mg concentration at ambient pressure shifts to higher frequencies with increasing pressure. (ii) The additional rocksalt modes of Zn0.90Mg0.10O appear at around 8.1 GPa. This
result indicates that the onset of the wurtzite-to-rocksalt phase transition of Zn0.90Mg0.10O is at lower pressure than that of ZnO
(∼9.6 GPa). (iii) The first-order Raman phonon modes in the wurtzite phase including the intense E2
low
and E2 high
modes vanish at 10.4 GPa. Also, the sample in the DAC suddenly changes from bright to dark, as shown in parts b and c of Figure 6, respectively. Restated, the metallic phase transition of the Zn0.90Mg0.10O is
complete at around 10.4 GPa, which value is lower than that of ZnO.
Before the effect of Mg on the phase transitions can be discussed, the downstroke pressure-dependent Raman spectra of ZnO and Zn0.90Mg0.10O, shown in parts a and b of Figure 7,
respectively, must be considered. Clearly, upon decompression, the rocksalt phase in both samples is maintained beyond the upstroke phase-transition pressure, revealing substantial phase hysteresis. The ZnO and Zn0.90Mg0.10O revert to the wurtzite
phase, in which the E2lowand E2highphononsfirst reappear, at about
2.4 and 1.2 GPa, respectively. Notably, the degree of phase hysteresis (the pressure difference between the end of the upward transition and the onset of downward transition) declines as Mg content increases. As the pressure is further released, the rest of the wurtzite-phase phonons, including the D mode appear. Once
Figure 5. (a) Upstroke pressure-dependent Raman spectra of ZnO. Asterisks indicate the 202.7 cm1phonon. (b) Pressure dependence of observed optical phonon frequencies. Solid lines are linear least-squarefits to experimental points.
the applied pressure is completely released, the samples behave in a time-independent manner, even after two months. Such an unusual hysteresis effect (>10 GPa) has also been observed in AlN, GaN, InN, and zincblende (3C-type) SiC.31,32 However, materials such as ZnSe, CdSe, and CdTe, exhibit quite small phase hysteresis (<3 GPa). This is because the lattice compressibilities of ZnSe (bulk modulus B0= 62.4 GPa), CdSe (B0= 53.1 GPa),
and CdTe (B0 = 42.4 GPa), which are considered to be softer
because of their lower moduli, greatly exceed those of 3C-SiC (B0= 321.9 GPa), AlN (B0= 208.0 GPa), GaN (B0= 200.0 GPa),
InN (B0= 125.5 GPa), and ZnO (B0= 135.3 GPa).18,27,3234
Table II summarizes the obtained upstroke and downstroke phase transition pressures for all the Zn1xMgxO samples.
Clearly, all of the phase-transition pressures fall with increasing Mg concentration. The differences between the atomic radii, masses, and electronegativities of Zn and Mg cause the crystal to become increasingly destabilized as the substituted Mg content increases. Moreover, the presence of Mg in ZnO may cause crystal defects (the D mode), which soften the lattice by generating large distortions and increase crystal anisotropy. These facts indicate that the substituted Mg atoms tend to reduce the crystalline
stability and induce crystal defects. Consequently, the phase transition pressures decline.
Table II lists the pressure coefficients (dωi/dp) and the mode
Gr€uneisen parameters (γi) of the Zn1xMgxO. The mode
Gr€uneisen parameter is defined by the relationship21
γi ¼ d lnωi d ln V ¼ B0 ωi dωi dp ! ð1Þ where B0 is the bulk modulus, defined as the reciprocal of
the isothermal compressibility. Since the bulk modulus of Zn1xMgxO is unavailable, the value of ZnO (B0= 135.3 GPa),
obtained from high-resolution XRD, is adopted for all of the samples.18 The influence of bulk modulus on the Gr€uneisen parameters can be disregarded herein due to low Mg concentra-tion (<10.0%). As presented in Table II, several conclusions can be drawn. (i) The phonon pressure coefficients, dωi/dp andγi,
for the E2lowphonons, are all negative. Moreover, the pressure
coefficients of dωi/dp for the E2high-E2lowmode agree excellently
with the differences between individual E2highand E2lowphonons.
These peculiar pressure-dependent phonon behaviors are strong
1 E1(TO) 4.95 1.63 E2(high) 4.77 1.47 D 4.61 1.22 A1(LO) 4.26 1.00 E1(LO) 4.49 1.03 7.0% E2(low) 0.68 0.92 8.5( 0.2a, 11.8( 0.2b, 1.8( 0.2c E2(high) E2(low) 5.41 2.21 A1(TO) 4.62 1.63 E1(TO) 4.97 1.63 E2(high) 4.70 1.45 D 4.64 1.23 A1(LO) 4.32 1.00 E1(LO) 4.60 1.04 10.0% E2(low) 0.66 0.88 8.1( 0.2a, 10.4( 0.2b, 1.4( 0.2c E2(high) E2(low) 5.33 2.18 A1(TO) 4.60 1.62 E1(TO) 4.96 1.62 E2(high) 4.62 1.43 D 4.62 1.22 A1(LO) 4.38 1.01 E1(LO) 4.71 1.06
aThe onset of wurtzite-to-rocksalt phase transition.bThefinish of wurtzite-to-rocksalt phase transition.cThe onset of rocksalt-to-wurtzite phase transition.
evidence of the assignment of the E2high-E2lowmode. (ii) The dωi/
dp andγiof the D mode remain nearly constant over the entire
Mg range of interest (0.03e x e 0.10). Moreover, its phonon pressure coefficient dωi/dp is very close to those of the A1(TO)
and E2highphonons, whose vibrations correspond mostly to the
oxygen atoms. These high-pressure experimental results further reveal that the Mg-induced complex ZnI-OIdefects with symmetry
different from the host lattice are most likely the original the D mode. (iii) For all samples, dωLO/dp < dωTO/dp andγLO<γTO,
indicating that the LO-TO splitting falls as the pressure increases. (iv) The pressure coefficients of the A1modes are all less than those
of the E1 modes, irrespective of their transverse or longitudinal
character, reflecting that the E1-A1splitting increases with pressure.
Figure 8a shows the pressure-dependent LO-TO splitting of Zn1xMgxO in E1mode. Clearly, the LO-TO splitting declines as
pressure increases. Similar results are also found in A1mode. The
result is consistent with observations of other IIVI compounds, such as ZnSe and ZnTe,21,30whose LO-TO splitting decreases with increasing pressure. However, the experimental results for ZnO differ from those in refs 14 and 15, implying that the pressure dependence of crystal ionicity in ZnO differs from those of their results. To study further the crystal ionicity of Zn1xMgxO, the transverse or Born effective charge (e*T), which
is defined as a dipole moment per unit displacement that is induced by slight movement of an atom, was calculated using the relation (in SI units)14
ðe TÞ
2 ¼ 4π2Vμε
0ε∞ðω2LO ω2TOÞ ð2Þ
where V is the volume per pair;μ is the reduced mass of an anioncation pair; ε0 is the vacuum permittivity;ε∞ is the
Figure 7. Downstroke pressure-dependent Raman spectra of (a) ZnO and (b) Zn0.90Mg0.10O. Black arrows indicate reappearance of E2lowand E2highphonons. Figure 6. (a) Upstroke pressure-dependent Raman spectra of
Zn0.90Mg0.10O. Asterisks mark 2E2lowphonon. Dashed arrow indi-cates behavior of D mode. Images of Zn0.90Mg0.10O powder under front illumination in DAC loaded with ruby chips at (b) ambient pressure and (c) 10.4 GPa.
Figure 8. Pressure dependence of (a) LO-TO splitting and (b) normal-ized transverse effective charge e*T/e*T(0) for E1mode in Zn1-xMgxO (0e x e 0.10). Solid lines are linear least-square fits to data points.
high-frequency dielectric constant, andωLO(ωTO) is the phonon
frequency. The reduced mass of Zn1xMgxO is given byμ = {MO
[xMMg+ (1 x)MZn]}/{MO+ [xMMg+ (1 x)MZn]}, where
MO, MZn, and MMgare the corresponding atomic weights. The
high-frequency dielectric constant of Zn1xMgxO is taken asε∞(x) =
(1 x)ε∞(ZnO) + xε∞(MgO), where the value ε∞(ZnO) =
3.70ε0andε∞(MgO) = 2.94ε0are used.35Table III presents the
calculated transverse effective charge values under ambient condi-tions. The values are 2.10e and 2.01e (where e is the elementary electron charge) in the ZnO A1and E1modes, respectively. These
values correlate closely with those in previous studies.14,16Similar to that associated with the LO-TO splitting, a slight increase in e*Tin
both A1and E1modes is found as the Mg content is increased. This
result is a consequence of an effective transfer of charge from the cation Zn to the anion O, which can be interpreted as ZnO’s becoming more ionic upon the incorporation of Mg. The degree of ionicity importantly affects the pressure-induced phase transition pressure. For example, the highly covalent material SiC starts to transform into the rocksalt phase at ∼100 GPa, and the reverse transition begins at ∼35 GPa.31However, the less covalent GaN undergoes upward and downward transitions at the much lower pressures of ∼37 and 25 GPa, respectively.31 The more ionic materials, such as MgO and CdO, favor the rocksalt phase at ambient pressure.23
Figure 8b plots the pressure-dependent transverse effective charge of Zn1xMgxO in E1mode. The dV/dp is described by the
Murnaghan equation of state,16 and the dε∞/dp = 0.014ε0
GPa1is used.14 For comparison, the e*Tis normalized to its
value at ambient pressure. The obtained values of the parameters de*T/dp,γeT*, and d[e*T/e*T(0)]/dp are negative for all of the
samples (Table III). Figure 8b also plots the experimental results for wurtzite AlN and GaN, and zincblende SiC and GaAs.14,16 Clearly, the e*T/e*T(0) of all the Zn1xMgxO falls under
com-pression, reflecting the fact that Zn1xMgxO becomes more
covalent at high pressures. This experimental result is similar to findings concerning GaAs and GaN but is in clear contrast to those of SiC and AlN. The decreasing ionicity is again in contrast with the result presented by Decremps et al., who found that e*T/
e*T(0) increased with pressure.14Interestingly, Mg and external
pressure oppositely affect the transverse effective charge of ZnO. At ambient pressure, ZnO becomes more ionic upon the incor-poration of Mg but becomes more covalent upon compression.
Consequently, the substituted Mg atoms tend to reduce the pressure dependence of the LO-TO splitting and of the trans-verse effective charge in Zn1xMgxO.
The crystal anisotropy, Δ(c/a), of a wurtzite structure is determined by the deviation of the c/a ratio from its ideal value (1.633):Δ(c/a) = c/a 1.633.36It is the crystal anisotropy that induces splitting of the A1 and E1 phonons. Therefore, for
Zn1xMgxO, a relationship may exist between the normalized
phonon frequency ratio [ωE1(TO) ωA1(TO)]/ωE1(TO) and
the crystal anisotropyΔ(c/a). Figure 9 plots the dependence of [ωE1(TO) ωA1(TO)]/ωE1(TO) on Δ(c/a) and pressure
for Zn0.90Mg0.10O using c/a = 1.602 and d(c/a)/dp =
0.0005 GPa1.36,37Significantly, a linear relationship is found
and afit of the experimental data to an equation of the form ½ωE1ðTOÞ ωA1ðTOÞ=ωE1ðTOÞ ¼ sΔðc=aÞ ¼ tPðGPaÞ ð3Þ
yielding the slope s = 1.59 and t = 7.92 104 cm1/GPa. Table IV presents the TO and LO phonon frequency ratios at ambient pressure and thefitted slopes for all of the samples. The TO (LO) phonon frequency ratios at ambient pressure are
1 0.36 0.26 13.0 0.84 6.21
10.0% A1 201.7 0.22 0.15 2.15 16.7 1.05 7.77
E1 187.3 0.26 0.19 2.11 12.0 0.77 5.69
aReference 14 (B
0= 170.0 GPa).bReference 16 (B0= 142.6 GPa).
Figure 9. Dependence of phonon frequency ratio [ωE1(TO) ωA1
0.048 (0.007), 0.061 (0.012), 0.074 (0.016), and 0.091 (0.021) for GaN,33InN,38 ZnO, and AlN,33respectively. These values qualitatively agree with the variation in Δ(c/a) for the above materials under ambient conditions.36 The results unambigu-ously demonstrate that the crystal anisotropy in ZnO exceeds that in GaN and InN but is less than that in AlN. On the basis of the overall phonon frequency ratios and thefitted slopes in Table IV, both Mg and pressure increase the crystal anisotropy of ZnO. Accordingly, a higher Mg content in Zn1xMgxO is clearly
associated with a higher rate at which the crystal becomes aniso-tropic, which fact is consistent with the Mg-induced decrease of the phase transition pressure.
’ CONCLUSIONS
We have studied the effects of both Mg and pressure on the lattice dynamics and crystalline properties in ZnO using Raman spectroscopy. On the basis of the distinct influences of Mg and external pressure on the lattice dynamic properties of ZnO, the vibrations at 202.7, 332.7, and 511.5 cm1can be assigned to 2E2low, E2high-E2low, and complex ZnI-OI phonons, respectively.
Detailed high-pressure Raman results reveal that the wurtzite-to-rocksalt phase transition pressure of ZnO is complete by around 13.2 GPa. As the Mg content increases from 0 to 10.0%, the phase transition pressure falls from 13.2 to 10.4 GPa. These results imply a decrease in the crystal stability as the Mg concentration increases. The transverse effective charge sub-stantially decreases as the pressure increases, yielding a trans-verse effective charge of 2.1019.3 103(e GPa1) and
2.0114.9 103(e GPa1) for the A
1 and E1 phonons,
respectively. Moreover, both the incorporated Mg and the applied pressure enhance the crystal anisotropy of ZnO. A higher Mg content in Zn1xMgxO is associated with a higher
rate at which the crystal becomes anisotropic. The above results are consistent with the Mg-induced reduction of the phase transition pressures.
The obtained phonon pressure coefficients are key parameters in determining strain levels and their distribution in Zn1xMgxO
heterostructures. They are also essential to understanding the phonon-plasmon interaction and to determining the electron or hole concentration (mobility) in Zn1xMgxO via a
nondestruc-tive Raman approach.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected] (Y.C.L.); wuchingchou@ mail.nctu.edu.tw (W.C.C).
’ ACKNOWLEDGMENT
This work was supported by the Ministry of Education and the National Science Council under Grant No. NSC 99-2119-M-009-002.
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Table IV. Dependence of the TO and LO Phonon Frequency Ratios on Crystal Anisotropy (in Terms of Slopes) and Pressure (in Terms of Slopet) for Zn1xMgxO
x = 0% x = 3.0% x = 7.0% x = 10.0% [ωE1(TO) ωA1(TO)]/ωE1(TO) 0.074 0.074 0.074 0.074
slope s 1.30 1.37 1.47 1.59
slope t (104cm1/GPa) 6.60 6.86 7.36 7.92 [ωE1(LO) ωA1(LO)]/ωE1(LO) 0.016 0.021 0.025 0.027
slope s 0.65 0.66 0.75 0.76
