Piezoelectric coefficient of GaN measured by laser interferometry
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Piezoelectric coecient 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,
Peoples Republic of Chinab Department of Electronic Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong,
Peoples Republic of Chinac SVT Associates, Inc., Eden Prairie, MN, USA
A MachZehnder type heterodyne interferometer was used to measure the d33 coecient of wurtzite gallium nitride
(GaN) films. The 140 nm thick GaN film, with a 30 nm thick aluminum nitride (AlN) buer layer, had been grown by
molecular beam epitaxy (MBE) on (1 0 0) or (1 1 1) silicon substrates. The measurement of the piezoelectric coecient
was made with a spatial resolution (laser beam diameter) of 100 lm. Voltage drop across the aluminum nitride buerlayer was estimated and used in calculating the piezoelectric coecient of GaN. For rigidly mounted samples, the
measured d33 was 2.13 pm/V. 1999 Elsevier Science B.V. All rights reserved.
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 . GaNhas a direct band gap of 3.39 eV  and has po-tential applications in devices working in hightemperature and hostile environments . Manydierent growth techniques have been used toprepare GaN films and molecular beam epitaxy(MBE) is one of the techniques that can give epi-taxial GaN films suitable for applications. Due toits properties, research in the physical propertiesand applications of GaN has attracted interest .
However, to date there appears to be limited dataon the piezoelectric coecients of GaN. Theseparameters are important since GaN has potentialuse in microactuators, microwave acoustic andmicroelectromechanical (MEM) devices .
2. Experimental details
2.1. Sample geometry
The 140 nm thick gallium nitride (GaN) filmswere grown by MBE on a 30 nm thick aluminumnitride (AlN) buer 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 dirac-tion (XRD) patterns of the GaN films grown on Si(1 1 1) and Si (1 0 0), respectively. The peak at 34.6
Journal of Non-Crystalline Solids 254 (1999) 123127
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0022-3093/99/$ see front matter 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) reflection of the wurt-zite GaN. The width of this reflection peak indi-cates that the film has good crystalline quality andare epitaxially grown with the c-axis orientedalong the normal (c) axis of the substrate . Anearby peak at 35.9 corresponds to the (0 0 0 2)reflection of the AlN buer layer .
Fig. 3 shows the sample geometry in the inter-ferometric measurements. The film sample has anarea of 10 10 mm. A number of aluminum spotsof diameter 1 mm were thermally evaporated onthe top surface of the film. Each of these spotsserves as a top electrode as well as a mirror toreflect the probe beam from the interferometer.The Si substrate was glued to an aluminum blockconnected to ground by silver filled epoxy whichwas in turn rigidly attached to a translation stage.An ac electric field was applied across the elec-
trodes and the change in the film thickness wasmeasured using a MachZehnder type heterodyneinterferometer.
2.2. Measurement of d33 using laser interferometery
Fig. 4 shows the MachZehnder 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 HeNe 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 film 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
J14pu=k=J04pu=k 2pu=k u=1007; 1where J0 and J1 are the Bessel function of thezeroth and the first order, respectively. The ratio ofamplitudes of zeroth order (center band) to firstorder (side band) of the Bessel function gives ab-solute displacement of sample surface. The ratio,R0 J14pu=k=J04pu=k in dBm can be measuredusing a spectrum analyzer (HP3589). LetR 10jR0 j=20, the vibration displacement is u 1007R0: 2The d33 coecient (strain/applied field) of the GaNAlN composite film (thickness t tGaN tAlN) canbe calculated as
Fig. 3. The sample geometry.
Fig. 1. The XRD pattern of GaN film grown on Si (1 1 1).
Fig. 2. The XRD pattern of GaN film grown on Si (1 0 0).
124 C.M. Lueng et al. / Journal of Non-Crystalline Solids 254 (1999) 123127
d33 u=t=V =t u=V ; 3where V VGaN VAlN is the voltage appliedacross the composite film. 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 . 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 eect is to re-duce the size of the electrode and to glue thesubstrate to a rigid holder . 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 dierent positions of the top
surface for use as electrodes as well as mirrors toreflect the probe beam. Measurements of the dis-placement amplitudes at these dierent 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 .
2.4. Eect of the AlN buer 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 d33GaNVGaN d33AlNVAlN; 4
where d33(GaN) and d33(AlN) are the piezoelectriccoecients of GaN and AlN, respectively. The
Fig. 4. A MachZehnder type heterodyne interferometer.
C.M. Lueng et al. / Journal of Non-Crystalline Solids 254 (1999) 123127 125
capacitance of each layer of the composite film 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, eGaN 8:9 and eAlN 8:5 , 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 d33AlN 5 pm/V, the d33 coecient of the GaN film can then becalculated.
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 film. Fig. 6shows the variation of the piezoelectric displace-ments with dierent driving voltages at 5 kHz
and the response is approximately linear. Fromthe slope of the line, the d33 coecient of theAlN/GaN composite film 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 coecient ofGaN film is calculated to be 2.13 0.05 pm/V.Fig. 7 shows that the measured piezoelectriccoecient is approximately independent of fre-quency from 5 to 10 kHz.
Fig. 6. Variation of the displacement with driving voltage at 5
kHz. The filled and open symbols represent GaN grown on Si
(1 1 1) and Si (1 0 0), respectively. The correlation coecients of
filled and open symbols are 0.9978 and 0.9930, respectively.
Fig. 7. Variation of the piezoelectric d33 coecient with fre-quency. The filled 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
126 C.M. Lueng et al. / Journal of Non-Crystalline Solids 254 (1999) 123127
In summary, the piezoelectric coecient d33 ofGaN films 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 coecient (2.0 pm/V) reported for GaN filmsgrown by chemical vapour deposition on n+ typeSi (1 0 0) .
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