Transcript

Piezoelectric coe�cient of GaN measured by laserinterferometry

C.M. Lueng a,*, H.L.W. Chan a, C. Surya b, W.K. Fong b, C.L. Choy a, P. Chow c,M. Rosamond c

a Department of Applied Physics, Materials Research Center, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong,

People's Republic of Chinab Department of Electronic Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong,

People's Republic of Chinac SVT Associates, Inc., Eden Prairie, MN, USA

Abstract

A Mach±Zehnder type heterodyne interferometer was used to measure the d33 coe�cient of wurtzite gallium nitride

(GaN) ®lms. The 140 nm thick GaN ®lm, with a 30 nm thick aluminum nitride (AlN) bu�er layer, had been grown by

molecular beam epitaxy (MBE) on (1 0 0) or (1 1 1) silicon substrates. The measurement of the piezoelectric coe�cient

was made with a spatial resolution (laser beam diameter) of 100 lm. Voltage drop across the aluminum nitride bu�er

layer was estimated and used in calculating the piezoelectric coe�cient of GaN. For rigidly mounted samples, the

measured d33 was 2.13 pm/V. Ó 1999 Elsevier Science B.V. All rights reserved.

1. Introduction

Gallium nitride (GaN) is a III-V nitride and thereported lattice parameters of GaN with wurtzitestructure are: a� 3.189 �A and c� 5.185 �A [1]. GaNhas a direct band gap of 3.39 eV [2] and has po-tential applications in devices working in hightemperature and hostile environments [3]. Manydi�erent growth techniques have been used toprepare GaN ®lms and molecular beam epitaxy(MBE) is one of the techniques that can give epi-taxial GaN ®lms suitable for applications. Due toits properties, research in the physical propertiesand applications of GaN has attracted interest [4].

However, to date there appears to be limited dataon the piezoelectric coe�cients of GaN. Theseparameters are important since GaN has potentialuse in microactuators, microwave acoustic andmicroelectromechanical (MEM) devices [5].

2. Experimental details

2.1. Sample geometry

The 140 nm thick gallium nitride (GaN) ®lmswere grown by MBE on a 30 nm thick aluminumnitride (AlN) bu�er layer. The substrates usedwere n+ type silicon with either (1 1 1) or (1 0 0)orientation. Figs 1 and 2 show the X-ray di�rac-tion (XRD) patterns of the GaN ®lms grown on Si(1 1 1) and Si (1 0 0), respectively. The peak at 34.6°

Journal of Non-Crystalline Solids 254 (1999) 123±127

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0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 3 8 3 - X

corresponds to the (0 0 0 2) re¯ection of the wurt-zite GaN. The width of this re¯ection peak indi-cates that the ®lm has good crystalline quality andare epitaxially grown with the c-axis orientedalong the normal (c) axis of the substrate [6]. Anearby peak at 35.9° corresponds to the (0 0 0 2)re¯ection of the AlN bu�er layer [7].

Fig. 3 shows the sample geometry in the inter-ferometric measurements. The ®lm sample has anarea of 10 ´ 10 mm. A number of aluminum spotsof diameter 1 mm were thermally evaporated onthe top surface of the ®lm. Each of these spotsserves as a top electrode as well as a mirror tore¯ect the probe beam from the interferometer.The Si substrate was glued to an aluminum blockconnected to ground by silver ®lled epoxy whichwas in turn rigidly attached to a translation stage.An ac electric ®eld was applied across the elec-

trodes and the change in the ®lm thickness wasmeasured using a Mach±Zehnder type heterodyneinterferometer.

2.2. Measurement of d33 using laser interferometery

Fig. 4 shows the Mach±Zehnder type hetero-dyne interferometer, (SH-120 from B.M. Indus-tries, France) which was used to measure thesurface displacement of the GaN sample. A lin-early polarized laser beam, L (frequency fL; wavenumber k� 2p/k, k� 632.8 nm for a He±Ne laser),is split into a reference beam, R, and a probebeam, P. R is directed through a Dove prism and apolarizing beam splitter into a photodiode. Thefrequency of P is shifted by a frequency fB (70MHz) in a Bragg cell, and then this beam (nowlabeled S), is phase modulated by the surface dis-placement of the ®lm sample, x� u cos(2pfut) (vi-bration frequency fu, displacement amplitude u).For small vibration displacement, u, only the sideband at fB + fu is detected and its amplitude is

J1�4pu=k�=J0�4pu=k� � 2pu=k � u=1007; �1�where J0 and J1 are the Bessel function of thezeroth and the ®rst order, respectively. The ratio ofamplitudes of zeroth order (center band) to ®rstorder (side band) of the Bessel function gives ab-solute displacement of sample surface. The ratio,R0 � J1�4pu=k�=J0�4pu=k� in dBm can be measuredusing a spectrum analyzer (HP3589). LetR � 10jR

0 j=20, the vibration displacement is [8]

u � 1007R0: �2�The d33 coe�cient (strain/applied ®eld) of the GaN±AlN composite ®lm (thickness t � tGaN � tAlN) canbe calculated as

Fig. 3. The sample geometry.

Fig. 1. The XRD pattern of GaN ®lm grown on Si (1 1 1).

Fig. 2. The XRD pattern of GaN ®lm grown on Si (1 0 0).

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d33 � �u=t�=�V =t� � u=V ; �3�where V � VGaN � VAlN is the voltage appliedacross the composite ®lm. V was measured usingan oscilloscope (Fig. 4) with a 50 X terminationconnected across the sample, to ensure when themeasurement frequency increases, the change insample impedance does not cause a change in thevoltage, V.

2.3. Sample mounting

When measuring the vibration displacementusing an interferometer, sample mounting is cru-cial to ensure that only the desired thickness modevibration is excited [9]. Other modes such as thebending mode may have a vibration amplitudebeing an order of magnitude larger than that of thethickness mode, hence, there is a larger error in themeasurement if the bending mode is also excited.One way to eliminate the bending e�ect is to re-duce the size of the electrode and to glue thesubstrate to a rigid holder [10]. To ensure that nobending mode was present, the probe beam wasscanned across the sample surface. As mentionedin the previous section, Al spots of diameter 1 mmwere deposited at di�erent positions of the top

surface for use as electrodes as well as mirrors tore¯ect the probe beam. Measurements of the dis-placement amplitudes at these di�erent positionsgave essentially the same results, indicating that nobending mode had been excited. The diameter ofthe probe beam, which corresponds to the spatialresolution of the measurement, was about 100 lm.As the electrode diameter was 1 mm, the probebeam was also scanned across each Al spot to testwhether bending vibration was excited within the 1mm spot. As shown in Fig. 5, the constant vibra-tion amplitudes observed imply that the dominantvibration is the thickness mode [9].

2.4. E�ect of the AlN bu�er layer

Since AlN is also piezoelectric, the displacementu � �uGaN � uAlN� measured by the interferometeris actually the resultant displacements of the twolayers. Assume that only the thickness vibration isexcited, then Eq. (3) gives

d33V � u � �uGaN � uAlN�� d33�GaN�VGaN � d33�AlN�VAlN; �4�

where d33(GaN) and d33(AlN) are the piezoelectriccoe�cients of GaN and AlN, respectively. The

Fig. 4. A Mach±Zehnder type heterodyne interferometer.

C.M. Lueng et al. / Journal of Non-Crystalline Solids 254 (1999) 123±127 125

capacitance of each layer of the composite ®lm canbe calculated using C � �e0eA�=t, where e0 is thepermittivity of free space, e is the relative permit-tivity of the material, A is the electrode area, and tis the thickness of the layer. Using the relativepermittivities from literature, e�GaN� � 8:9 [11]and e�AlN� � 8:5 [12], tGaN � 140 nm, tAlN � 30nm, the capacitances of the AlN and GaN layerswere calculated to be 1.97 and 0.42 nF, respectively.For two capacitors in series, CGaNVGaN � CAlNVAlN,hence if a voltage V is applied across the compositelayer, then VGaN=V � 0:82 and VAlN=V � 0:18.Using Eq. (4) and the literature d33�AlN� � 5 pm/V[13], the d33 coe�cient of the GaN ®lm can then becalculated.

3. Results

The electrical impedance and phase angle ofthe samples were measured as functions of fre-quency using an impedance analyzer (HP4194A).No resonance peak was observed in the frequencyrange from 5 to 10 kHz, indicating that there wasno mechanical resonance in this frequency region.Subsequent measurements were made at thecenter of a 1 mm diameter aluminum electrodelocated close to the center of the ®lm. Fig. 6shows the variation of the piezoelectric displace-ments with di�erent driving voltages at 5 kHz

and the response is approximately linear. Fromthe slope of the line, the d33 coe�cient of theAlN/GaN composite ®lm is found to be2.65 � 0.05 pm/V for both Si (1 1 1) and Si (1 0 0)substrates. Using Eq. (4), the d33 coe�cient ofGaN ®lm is calculated to be 2.13 � 0.05 pm/V.Fig. 7 shows that the measured piezoelectriccoe�cient is approximately independent of fre-quency from 5 to 10 kHz.

Fig. 6. Variation of the displacement with driving voltage at 5

kHz. The ®lled and open symbols represent GaN grown on Si

(1 1 1) and Si (1 0 0), respectively. The correlation coe�cients of

®lled and open symbols are 0.9978 and 0.9930, respectively.

Fig. 7. Variation of the piezoelectric d33 coe�cient with fre-

quency. The ®lled and open symbols represent GaN grown on

Si (1 1 1) and Si (1 0 0), respectively.

Fig. 5. Variation of the amplitude of vibration across the sur-

face of a 1 mm diameter Al electrode near the centre of the GaN

®lm.

126 C.M. Lueng et al. / Journal of Non-Crystalline Solids 254 (1999) 123±127

4. Conclusion

In summary, the piezoelectric coe�cient d33 ofGaN ®lms grown on (1 0 0) and (1 1 1) Si substrateshas been measured by the laser interferometricmethod and 2.13 pm/V is obtained for both sub-strates. This d33 is approximately the same as thed33 coe�cient (2.0 pm/V) reported for GaN ®lmsgrown by chemical vapour deposition on n+ typeSi (1 0 0) [9].

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