Reduction of the transverse effective charge of optical phonons in ZnO under pressure [original]

Appl. Phys. Lett. 96, 231906 (2010); https://doi.org/10.1063/1.3447798 96, 231906

Reduction of the transverse effective

charge of optical phonons in ZnO under

pressure

Cite as: Appl. Phys. Lett. 96, 231906 (2010); https://doi.org/10.1063/1.3447798

Submitted: 19 April 2010 . Accepted: 18 May 2010 . Published Online: 09 June 2010

J. S. Reparaz, L. R. Muniz, M. R. Wagner, A. R. Goñi, M. I. Alonso, A. Hoffmann, and B. K. Meyer

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Reduction of the transverse effective charge of optical phonons in ZnO

under pressure

J. S. Reparaz,1,a兲L. R. Muniz,2M. R. Wagner,1A. R. Goñi,2M. I. Alonso,2A. Hoffmann,1

and B. K. Meyer3

1Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany

2Institut de Ciència de Materials de Barcelona–CSIC, Esfera UAB, 08193 Bellaterra, Spain

3I. Physics Institute, Justus Liebig University, Heinrich-Buff-Ring 16, 35592 Giessen, Germany

共Received 19 April 2010; accepted 18 May 2010; published online 9 June 2010兲

From Raman scattering on a-plane wurtzite ZnO crystals we obtained a decreasing splitting between

longitudinal and transversal optical phonons with A1and E1symmetry as a function of hydrostatic

pressure up to 5.5 GPa. Consequently, the transverse effective charge 共eT

ⴱ兲exhibits a strong

reduction with increasing pressure, yielding 2.17–14.6⫻10−3 P/GPa and 2.04–13.7

⫻10−3 P/GPa 共in units of the elementary charge兲for the A1and E1phonons, respectively. We find

a clear systematic in the linear pressure coefficient of eT

ⴱwith bond polarity for the series of

关doi:10.1063/1.3447798兴

ZnO is a semiconductor material which has drawn re-

newed attention due to its promising integration into opto-

electronic devices. Its large band gap of about 3.3 eV at room

temperature, its structural compatibility with GaN, and its

low production cost are some of the properties that make this

system interesting for sensor applications.1In addition, its

nontoxicity and biocompatibility with organic systems have

been only recently discussed,2,3pointing to ZnO as a prom-

ising candidate for hybrid devices. For many applications a

fundamental understanding of the thermal, optoelectronic,

and mechanical properties of this system is mandatory. At

ambient conditions the thermodynamically stable crystal

phase of ZnO is the wurtzite structure. Recently, the me-

chanical properties of ZnO have been investigated up to 60

GPa.4The initial wurtzite phase was observed to transform to

the rocksalt structure around 9.1 GPa with a large volume

collapse of 16.7% on increasing pressure. The wurtzite struc-

ture belongs to the C6v

4space group with four atoms per unit

cell. From the 12 possible vibrational modes only the A1,E1,

and E2are Raman-active optical modes. The ionic character

of the Zn–O bonds is responsible for the large splitting of the

polar modes 共A1and E1兲into longitudinal optical 共LO兲and

transverse optical 共TO兲. The Born’s transverse effective

charge 共eT

ⴱ兲of the lattice ions is determined by the LO–TO

splitting, the screening of the Coulomb interaction 共which

depends on the electronic part of the dielectric function

⑀

⬁兲,

and the volume of the unit cell.5All three parameters depend

on pressure but is the LO–TO splitting the one dictating the

qualitative behavior of eT

ⴱat reduced volumes.

In a recent work6the hydrostatic pressure dependence of

the Raman optical modes of wurtzite ZnO was investigated

up to 9 GPa. Surprisingly, the authors found that the LO–TO

splitting increases with increasing pressure for the E1modes.

This result is in clear contrast with observations made for

other II–VI compounds such as ZnSe 共Ref. 7兲and ZnTe,7

where the LO–TO splitting decreases with pressure. The

Born’s transverse effective charge 共which is computed from

the value of the LO–TO splitting兲was also shown to increase

with pressure 共deT

ⴱ/dP⬎0兲. This result is again difficult to

match with previous observations in GaN,8AlN,8GaAs,9and

GaP,10 where eT

ⴱwas shown to decrease with pressure or at

most to remain nearly constant. So far the only known ma-

terial which exhibits a positive pressure derivative deT

ⴱ/dP

⬎0 is SiC. In this particular case, this effect was suggested

to be a consequence of the lack of pelectrons in the carbon

cores, which allows for a larger penetration of the Si wave

functions into that regions.8,11 In spite of the fact that the

same argument would apply to the oxygen cores of ZnO, the

problem is that the reported value for deT

ⴱ/dP in Ref. 6is

larger than that of SiC even though the bond polarity of ZnO

is much higher than for SiC and for the nitrides as well,

which exhibit deT

ⴱ/dP⬇0. This apparent inconsistency was a

strong motivation for revisiting the pressure dependence of

ⴱin ZnO crystals.

In this letter, we report the dependence on hydrostatic

pressure of the zone-center optical phonons of wurtzite ZnO

crystals as obtained from Raman measurements. From a de-

tailed line shape analysis of the Raman spectra we were able

to determine the Grüneisen parameters as well as the pres-

sure dependence of the LO–TO splitting for both polar A1

and E1modes. The Born’s transverse effective charge was

found to decrease with increasing pressure for both modes,

displaying a clear systematic behavior of deT

ⴱ/dP as a func-

tion of bond polarity 共as defined in Ref. 12兲for the whole

series of materials from SiC, AlN, and GaN to ZnO.

Raman spectra were collected at room temperature with

a LabRam HR800 system in backscattering geometry from

an a-plane surface. In this configuration the caxis of the ZnO

crystal is perpendicular to the direction of incidence of the

laser light. The 514.5 nm line of an Ar+laser was used for

excitation, focused onto the sample using a long distance

20⫻Olympus objective. Raman peak positions were deter-

mined with an error of less than 0.5 cm−1. Measurements

under pressure were carried out using the diamond anvil cell

共DAC兲technique. A 4:1 mixture of methanol and ethanol

was employed as the pressure-transmitting medium. Pressure

was monitored in situ by the shift in the ruby R1line.13 An

a-plane wurtzite ZnO crystal purchased from Crystec was

a兲Electronic mail: [email protected].

APPLIED PHYSICS LETTERS 96, 231906 共2010兲

thinned to about 30

␮

mby mechanical polishing and loaded

into the DAC.

Figure 1shows three representative Raman spectra from

the a-plane surface at different pressures of 0.1, 2.5, and 4.8

GPa. For this configuration the only allowed optical Raman

modes are the E2

high,E2

low,A1共TO兲, and E1共TO兲.14 Neverthe-

less, the A1共LO兲and E1共LO兲are also observed in the spectra

due to the large angular aperture of the focusing objective

共NA=0.35兲, which leads to a partial lifting of selection rules

by departure from strict normal incidence. In the present

case, this represents an advantage since it allows for a pre-

cise determination of the LO–TO splittings. The peak posi-

tions were determined by fitting every spectrum using

Lorentzian line shapes for A1,E1, and E2

low phonons. For the

high mode, however, we used a Fano profile, since in the

lower pressure regime 共P⬍3 GPa兲its line shape is strongly

influenced by anharmonic effects, due to its decay into a sum

of transverse and longitudinal acoustic phonons 共TA+LA兲in

the vicinity of the Kpoint of the Brillouin zone.15

Figure 2displays the dependence on hydrostatic pressure

of the main first-order Raman modes. We only show data in

the pressure range up to 5.5 GPa, for which the pressure

dependence of all peaks is well described by a straight line.

The solid lines in Fig. 2represent the results of least-squares

fits to the data points using a linear relation. Table Ishows

the results for

␻

0and

⳵␻

⳵

Ptogether with previous results

for comparison.6From the obtained data we computed the

mode-Grüneisen parameter as

␥

i=d关ln共

␻

i兲兴/d关ln V兴

⬇共B0/

␻

i兲⫻

⳵␻

⳵

P, where

␻

iis the mode frequency, B0is

the bulk modulus, and Pis the pressure. For the isothermal

bulk modulus we used the value of B0=142.6共2兲GPa, as

measured by x-ray diffraction.4The discrepancy in the deter-

mination of the Grüneisen parameters with Ref. 6共see Table

I兲stems from a different choice of B0, and also from the

inaccuracy in the determination of the phonon pressure co-

efficient. Concerning B0, Ref. 4represents the state of the art.

The indetermination in the pressure coefficients is substan-

tially reduced in our measurements due to the clear observa-

tion of every peak in the Raman spectra measured with the

DAC and due to the fitting procedure used to determine the

peak positions.

We now turn to the discussion of the LO–TO splitting of

the A1and E1phonons. Figure 3displays the pressure depen-

dence of the LO–TO splitting with similar pressure behavior

for both modes. In spite of the scatter of the data, it is clear

that the splitting diminishes under pressure in both cases.

Concerning the discrepancy between our results and those of

Ref. 6, we conclude that the problem lies most probably in

the determination of the pressure coefficient of E1共TO兲.In

their case, the E1共TO兲phonon was hardly seen at room tem-

perature such that its apparent frequency position was

strongly affected by the large asymmetric Fano-like profile

of the E2

high mode.15

TABLE I. Coefficients from the linear fits to the data points of Fig. 2using

␻

0+共

⳵␻

⳵

P兲P and correspond-

ing Grüneisen parameters 共frequencies in cm−1 and pressures in GPa兲. For comparison we list results from Ref.

6. Numbers in parenthesis are error bars.

Mode

␻

⳵␻

⳵

␥

⳵␻

⳵

␥

low 98.1 ⫺0.78共2兲⫺1.13共4兲⫺0.93 ⫺1.6

high 437.9 5.04共3兲1.63共1兲5.16 2

A1共TO兲377.4 4.91共5兲1.85共2兲4.72 2.1

E1共TO兲410.9 5.03共3兲1.74共1兲4.38 1.8

A1共LO兲577.9 4.56共7兲1.12共2兲¯¯

E1共LO兲587.2 4.55共10兲1.11共3兲4.78 1.4

aReference 6.

100 200 300 400 500 600

2TA, 2Elow

low

, 2LA

high

-E

low

(LO)

(TO)

4.8 GPa

2.5 GPa

Intensity

(

arb. units

)

Raman Shift

(

cm-1

)

0.1 GPa

ZnO a-plane

300 K

high

FIG. 1. Representative Raman spectra of an a-plane wurtzite ZnO crystal at

three different pressures of 0.1, 2.5, and 4.8 GPa. The spectra were vertically

shifted for clarity. Fits to the first order Raman peaks are shown as example

for the 4.8 GPa spectrum.

012345

100

350

400

450

500

550

600

Elow

ZnO a-plane

300 K

E1(LO

)

A1(LO

)

Ehigh

A1(TO)

E1(TO)

Raman Shift(cm

)

Pressure

(

GPa

)

FIG. 2. 共Color online兲Pressure dependence of the first-order Raman modes.

Solid lines are results of least-squares fits to the data points using linear

relations.

231906-2 Reparaz et al. Appl. Phys. Lett. 96, 231906 共2010兲

The Born’s transverse effective charge can be calculated

according to 共in SI units兲the following:5

共eT

ⴱ兲2=␧0␧⬁V

␮

共

␻

2−

␻

2兲,共1兲

where ␧0is the vacuum permittivity, ␧⬁is the high frequency

dielectric constant,

␮

is the reduced mass of the anion–cation

pair, Vis the volume per pair, and

␻

LO,TO is the correspond-

ing phonon frequency. For the pressure dependence of the

unit-cell volume we used the Murnaghan equation of state16

and the bulk modulus from Ref. 4. Unfortunately, for the

pressure dependence of ␧⬁there are no high-pressure data

available. Nevertheless, we used the pressure dependence of

the refractive index at optical frequencies n0measured in the

range up to 0.7 GPa 共Ref. 17兲to obtain 共

⳵

␧⬁/

⳵

P兲

=−0.014 GPa−1. A close inspection of the Eq. 共1兲indicates

that for ZnO eT

ⴱmust decrease with increasing pressure since

all involved parameters do as well. The relative contribution

of each of these parameters to the pressure dependence of eT

ⴱ

is readily estimated to be about 17%, 29%, and 54% for the

mode splitting, the dielectric constant, and the volume, re-

spectively. The results obtained for the transverse effective

charge of ZnO normalized to its zero-pressure value are plot-

ted in Fig. 4as a function of pressure together with the data

for SiC, AlN, GaN, and GaAs extracted from Refs. 8,9, and

11. For completeness the values at ambient pressure are

ⴱ共0兲共A1兲=2.17⫻10−3e0and eT

ⴱ共0兲共E1兲=2.04⫻10−3e0, with

e0the elementary electron charge. We point out that there is

a clear systematic in the magnitude and sign of the pressure

coefficient of the transverse effective charge for the series

SiC, AlN, GaN, and ZnO 共see Fig. 4兲. Considering the bond

polarity

␣

pas defined by Harrison12 we obtain for the previ-

ous series

␣

p=0.26, 0.58, 0.60, and 0.78, respectively. This

might indicate that for the heteropolar semiconductor com-

pounds of the form ANB8−Nwith anion species belonging to

the first row of the periodic table the transverse effective

charge exhibits the following lattice-constant scaling: for

bond polarities lower than 0.6, eT

ⴱincreases with pressure in

inverse proportion to the bond polarity. Otherwise, the de-

crease in eT

ⴱis the stronger, the larger the polarity.

In conclusion, we have revisited the pressure depen-

dence of the zone center optical phonons of ZnO using

wurtzite a-plane crystals. The LO–TO splitting of the polar

modes E1and A1exhibit a moderate decrease with increasing

pressure. Consequently, the Born’s transverse effective

charge also decreases at reduced volumes and its pressure

coefficient fits well into a systematic observed for the semi-

conductor compound series of SiC, AlN, GaN, and ZnO as a

function of bond polarity.

A.R.G. is an ICREA Research Professor. This work was

supported in part by the Spanish Ministerio de Ciencia e

Innovación through Grant No. MAT2009-09480 and Ac-

ciones Integradas Hispano-Alemanas 2007, and by DFG

within Grant No. SFB787. Measurements were performed at

MATGAS 2000 A.I.E.

1Ü. Özgür, Y. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Doğan, V.

Avrutin, S.-J. Cho, and H. Morkoç, J. Appl. Phys. 98, 041301 共2005兲.

2H. J. Bolink, E. Coronado, D. Repetto, and M. Sessolo, Appl. Phys. Lett.

91, 223501 共2007兲.

3C. Lao, Y. Li, C. P. Wong, and Z. L. Wang, Nano Lett. 7,1323共2007兲.

4S. Desgreniers, Phys. Rev. B 58, 14102 共1998兲.

5P. Y. Yu and M. Cardona, Fundamentals of Semiconductors 共Springer,

Berlin, 1996兲, p. 293.

6F. Decremps, J. Pellicer-Porres, A. M. Saitta, J. C. Chervin, and A. Polian,

Phys. Rev. B 65, 092101 共2002兲.

7S. S. Mitra, O. Brafman, W. B. Daniels, and R. K. Crawford, Phys. Rev.

186, 942 共1969兲.

8A. R. Goñi, H. Siegle, K. Syassen, C. Thomsen, and J.-M. Wagner, Phys.

Rev. B 64, 035205 共2001兲.

9R. Trommer, H. Müller, M. Cardona, and P. Vogl, Phys. Rev. B 21, 4869

共1980兲.

10B. A. Weinstein and G. J. Piermarini, Phys. Rev. B 12, 1172 共1975兲.

11D. Olego, P. Vogl, and M. Cardona, Phys. Rev. B 25, 3878 共1982兲.

12W. A. Harrison, Electronic Structure and The Properties of Solids 共Dover,

New York, 1989兲, p. 175.

13H. K. Mao, J. Xu, and P. M. Bell, J. Geophys. Res. 91, 4673 共1986兲.

14R. Cuscó, E. Alarcón-Lladó, L. Artús, J. Ibáñez, J. Jimenez, B.-G. Wang,

and M. J. Callahan, Phys. Rev. B 75, 165202 共2007兲.

15J. Serrano, F. J. Manjon, A. H. Romero, F. Widulle, R. Lauck, and M.

Cardona, Phys. Rev. Lett. 90, 055510 共2003兲.

16F. D. Murnaghan, Proc. Natl. Acad. Sci. U.S.A. 30, 244 共1944兲.

17K. Vedam and T. A. Davis, Phys. Rev. 181,1196共1969兲.

012345

170

175

195

200

ZnO a-plane

300 K

A1: -0.36(10) cm-1GPa-1

LO - TO Splitting (cm

-1

)

Pressure (GPa)

: -0.47(7) cm

-1

GPa

-1

FIG. 3. 共Color online兲Pressure dependence of the LO–TO splitting for the

polar A1and E1phonons. Solid lines are results of least-squares fits to the

data points using linear relations.

012345

0.94

0.96

0.98

1.00

3C-GaAs

E1: -6.3(2)x10-3GPa-1

A1: -6.7(2)x10-3GPa-1

2H-GaN, A1

2H-AlN, E1

Normalized Transverse

Effective Charge e

*/e

*(0)

Pressure

(

GPa

)

3C-SiC

2H-ZnO

FIG. 4. 共Color online兲Dependence on pressure of the transverse effective

charge normalized to its ambient pressure value. For comparison the dotted

lines correspond to the experimental results obtained for SiC, AlN, GaN,

and GaAs extracted from Ref. 8.

231906-3 Reparaz et al. Appl. Phys. Lett. 96, 231906 共2010兲