APPLIED PHYSICS LETTERS
VOLUME 75, NUMBER 26
27 DECEMBER 1999
Extensional piezoelectric coefficients of gallium nitride and aluminum nitride I. L. Guy, S. Muensit,a) and E. M. Goldysb) Semiconductor Science and Technology Laboratories, Macquarie University, North Ryde, NSW 2109, Australia
共Received 28 June 1999; accepted for publication 3 November 1999兲 Measurements of piezoelectric coefficients d 33 and d 31 in wurtzite GaN and AlN using an c of these coefficients interferometric technique are presented. We report on the clamped values, d 33 b . The clamped value found in GaN and AlN thin films, and we derive the respective bulk values, d 33 c in GaN single crystal films is 2.8⫾0.1 pm V⫺1 which is 30% higher than in polycrystalline of d 33 b in bulk single crystal GaN films grown by laser assisted chemical vapor deposition. The value of d 33 c ⫺1 is found to be 3.7⫾0.1 pm V . The value of d 33 in plasma assisted and laser assisted chemical vapor deposited AlN films was 3.2⫾0.3 and 4.0⫾0.1 pm V⫺1, respectively. The bulk value estimate b in AlN of 5.6⫾0.2 pm V⫺1 was deduced. The values of d 31 , both clamped and bulk, were of d 33 calculated for wurtzite GaN and AlN. We have also calculated the values of d 14 in cubic phase film and bulk GaN and AlN. Interferometric measurements of the inverse piezoelectric effect provide a simple method of identifying the positive direction of the c axis, which was found to be pointing away from the substrate for all films. © 1999 American Institute of Physics. 关S0003-6951共99兲01552-1兴
We examined GaN and AlN films grown by a range of methods. Polycrystalline wurtzite 关0002兴 1-m-thick GaN was grown on 关100兴 doped silicon by laser assisted chemical vapor deposition.9 A single crystal 2.5-m-thick 关0001兴 GaN film grown on silicon carbide by hydride vapor phase epitaxy, was obtained from Technologies and Devices International, Inc., USA. Two samples of polycrystalline AlN films grown on doped 关100兴 silicon were used.10 The first film was grown by chemical vapor deposition at 200 °C, it was 1 m thick and had a 0.1 m oxide layer on the surface. The second sample was grown by microwave plasma assisted chemical vapor deposition, at temperatures below 90 °C.11 X-ray diffraction spectra of both films confirmed the wurtzite structure and 关0001兴 orientation. The piezoelectric tensor component measured was d 33 . For the wurtzite structure, the three direction is associated with the direction of the crystallographic c axis. If an electric field is applied parallel to the c axis, the d 33 coefficient can be obtained directly from the ratio of the resultant displacement normal to the film plane, to the applied voltage. In wurtzite crystals the component d 31 can be obtained from d 33 by the relation12,13
To date, there are no experimental values available for the piezoelectric coefficients of GaN, apart from our earlier work on a polycrystalline material.1 Likewise, very few reports have appeared on the piezoelectric coefficients for AlN. Given the level of current interest in nitride-based devices, such as high electron mobility transistors 共HEMTs兲,2 experimental values for the piezoelectric coefficients are of considerable interest. The piezoelectric tensor of wurtzite GaN and AlN crystals d i j has three different nonzero components 共piezoelectric strain coefficients兲: d 33 , d 31(⫽d 32), and d 15(⫽d 24). 3 Sometimes the piezoelectric stress coefficients e i j are used, these are related to d i j through a tensor relationship4 E e ip ⫽⌺ q d iq c qp ,
共1兲
where c E is the elastic stiffness tensor at constant electric field. A summary of the d i j and e i j coefficients for GaN and AlN, as reported in the literature, is given in Table I. We measured the inverse piezoelectric effect by applying an external electric field across the film thickness. This induces strain in the films, leading to surface displacement which was measured by an interferometric technique. The experimental system was based on a single beam Michelson–Morley laser interferometer with active adjustment of the optical path length to compensate slow drifts. Measurements were made at frequencies ranging from 1 to 100 kHz and surface displacements as small as 3⫻10⫺3 Å could be reliably measured. Details of the technique have been described earlier.2 Bending mode vibrations were observed above 50 kHz and all measurements reported here were obtained over the range from 1 to 10 kHz.
d 31⫽⫺ 21 d 33 .
All the films used in the present work were deposited on substrates, which restrict the strain in the plane of the films and this in turn reduces the strain along the c axis. The result c , is less than the is that the measured clamped coefficient, d 33 b . For wurtzite value for the unconstrained bulk material, d 33 crystals these are related by14 b c d 33 ⫽d 33
a兲
Present address: Physics Department, Prince of Songkla University, Hatyai 90112 Thailand. b兲 Electronic mail:
[email protected] 0003-6951/99/75(26)/4133/3/$15.00
共2兲
冉
E E s 11 ⫹s 12 E E E s 11⫹s 12⫹s 13
冊
.
共3兲
Here s E is the elastic compliance tensor at constant electric field.15–17 4133
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© 1999 American Institute of Physics
4134
Appl. Phys. Lett., Vol. 75, No. 26, 27 December 1999
Guy, Muensit, and Goldys
TABLE I. Values of extensional piezoelectric coefficients in wurtzite GaN and AlN reported earlier and obtained in this work.
GaN Bulk Clamped single crystal Clamped polycrystalline AlN
Bulk Clamped grown at 200 °C Clamped grown at 90 °C
d 33 (pm V⫺1)
d 13 (pm V⫺1)
e 33 (cm⫺2)
e 31 (cm⫺2)
3.7 b 2.8⫾0.1 b
⫺1.9 b ⫺1.4⫾0.1 b
0.73 a 1.12 b 0.85 b
⫺0.49 a ⫺0.55 b ⫺0.41 b
2.0⫾0.1 b,c
⫺1.0⫾0.1 b,c
0.60 b
⫺0.30 b
5d 5.53 e 6.72 f 5.6 c 4.0⫾0.1 c
⫺2 d ⫺2.65 e ⫺2.71 f ⫺2.8 c ⫺2.0⫾0.1 c
1.46 a
⫺0.60 a
1.5 1.06
⫺0.60 ⫺0.63
3.2⫾0.3 c
⫺1.6⫾0.1 c
0.85
⫺0.5
FIG. 2. Variations of mechanical displacement with driving voltage measured for frequencies in the range from 1 to 10 kHz for the single crystal GaN film.
a
See Ref. 8. This work. c See Ref. 2. d See Ref. 5. e See Ref. 6. f See Ref. 7. b
Figure 1 shows the piezoelectric response in the polycrystalline GaN film for applied fields from 0.2 to 60 c for this film, obtained by MV m⫺1. The clamped value of d 33 averaging over the frequency range from 1 to 10 kHz, was (2.0⫾0.1) pm V⫺1. Figure 2 shows the response obtained with the single crystal GaN film in the frequency range from c , averaged over 1 to 10 kHz. The clamped value of the d 33 this frequency range, was found to be (2.8⫾0.1) pm V⫺1. Similar plots to those shown in Figs. 1 and 2 were obtained for the AlN films. The slopes of these plots gave valc ues for the clamped d 33 of (3.2⫾0.3) pm V⫺1 for the 90 °C grown film and (4.0⫾0.1) pm V⫺1 for the film grown at 200 °C. The observed response for the 200 °C film was linear for fields from 0.1 to 60 MV m⫺1, while that for the 90 °C film was nonlinear at low fields. This is reflected in the larger uncertainty of the value for this film. As the 200 °C film was c gives a better estimate of the true value of less porous, its d 33 the piezoelectric coefficient in AlN. c The value of d 31 for all films was calculated using Eq. 共2兲 共see Table I兲.
c We have further used the clamped values of d 33 to derive the respective bulk values. These were calculated from Eq. b was calculated using Eq. 共2兲. In 共3兲 and then a value of d 31 c from the single crystal the calculations, the values of the d 33 GaN film and from the 200 °C grown AlN were used, as more reliable. For the elastic coefficients we have used the values given by Wright,16 which fall within the range of b b and d 31 coefother published values. The values of the d 33 ficients for bulk GaN were found to be 3.7 and ⫺1.9 b b and d 31 for ⫾pm V⫺1, respectively. The values of the d 33 bulk AlN are 5.6 and ⫺2.8 pm V⫺1, respectively. Table I summarizes our results. Finally, we have determined the piezoelectric coefficient d 14 of zinc-blende GaN and AlN. The relationship between the piezoelectric coefficients of each structure is given by12,13 ZB W d 14 ⫽)d 33 .
共4兲
Here the index W indicates the wurtzite phase, while ZB indicates the zinc-blende phase. Subsequently, e 14 can be obtained from d 14 using the relation E e 14⫽d 14c 44 ,
共5兲
E is the component of a stiffness tensor at a constant where c 44 electric field. The calculated zinc-blende coefficients are summarized in Table II. In the 6 mm crystal class, the positive direction of the c axis is defined in such a way as to make d 33 positive.4 In the interferometric measurements, the phase of the detector voltage is determined by the sign of d 33 and the orientation of the c axis. The orientation of the c axis could thus be determined by comparing the phase in the examined films with that from a known sample. In all the films studied, the positive direction of the c axis was found to point away from the substrate.
TABLE II. Values of the extensional piezoelectric coefficients in cubic GaN and AlN obtained in this work.
FIG. 1. Surface displacement vs driving voltage at 1 kHz for the polycrystalline GaN film.
GaN, bulk AlN, bulk
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d 14 (pm V⫺1)
e 14 (cm⫺2)
6.4⫾0.2 9.7⫾0.3
0.61 1.13
Appl. Phys. Lett., Vol. 75, No. 26, 27 December 1999
In summary, we report the measurements of piezoelectric coefficients in AlN and single crystal GaN by interferometry. These measurements represent an extension of the work reported in our earlier publication1 where the clamped c in a polycrystalline GaN film was given. We value of d 33 emphasize that in estimates of the piezoelectric field in structures grown on substrates, for example in strained GaN/ AlGaN quantum wells or in the GaN/AlGaN HEMTs, the clamped values should be used, whereas, for example in calculations of piezoelectric contribution to charge carrier mobilities in bulk materials, it is necessary to use the bulk values. S. Muensit and I. L. Guy, Appl. Phys. Lett. 72, 1896 共1998兲. R. Gaska, M. S. Shur, T. A. Fjeldly, and A. D. Bykhovski, J. Appl. Phys. 85, 3009 共1999兲. 3 J. F. Nye, Physical Properties of Crystals 共Oxford University Press, New York, 1985兲, p. 124. 1 2
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IEEE Standard on Piezoelectricity (ANSI/IEEE Standard 176-1987) 共The Institute of Electrical and Electronics Engineers, Inc., New York, 1988兲. 5 A. R. Hutson, US Patent No. 3,090,876 共21 May 1963兲. 6 K. Tsubouchi, K. Sugai, and N. Mikoshiba, Proceedings of the IEEE Ultrasonic Symposium 共IEEE, New York, 1982兲, p. 340. 7 T. Kamiya, Jpn. J. Appl. Phys., Part 1 35, 4421 共1996兲. 8 F. Bernardini, V. Fiorentini, and D. Vanderbilt, Phys. Rev. B 56, R10024 共1997兲. 9 B. Zhou, X. Li, and K. S. A. Butcher, J. Cryst. Growth 160, 201 共1996兲. 10 X. Li and T. L. Tansley, J. Appl. Phys. 68, 5369 共1990兲. 11 K. S. A. Butcher, T. L. Tansley, and X. Li, Surf. Interface Anal. 25, 99 共1997兲. 12 J. L. Birman, Phys. Rev. 111, 1510 共1958兲. 13 D. Berlincourt, H. Jaffe, and L. R. Shiozawa, Phys. Rev. 129, 1009 共1963兲. 14 D. Royer and V. Kmetik, Electron. Lett. 28, 1828 共1992兲. 15 Y. Takagi, M. Ahart, T. Azuhata, T. Sota, K. Suzuki, and S. Nakamura, Physica B 219–220, 547 共1996兲. 16 A. F. Wright, J. Appl. Phys. 82, 2833 共1997兲. 17 E. Ruiz, S. Alvarez, and P. Alemany, Phys. Rev. B 49, 7115 共1994兲. 4
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