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AlGaSb cantilevers
Applied Surface Science 237 (2004) 649–653 www.elsevier.com/locate/apsusc
Mechanical and piezoresistive properties of InAs/AlGaSb cantilevers H. Yamaguchia,*, S. Miyashitab, Y. Hirayamaa,c a
NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan b NTT Advanced Technology, Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan c Core Research for Evolutional Science and Technology (CREST), JST, Japan Available online 4 August 2004
Abstract We fabricated piezoresistive micromechanical cantilevers using InAs/AlGaSb heterostructures grown by molecular beam epitaxy on GaAs (1 1 1) A and (0 0 1) substrates. The piezoresistance allows the cantilever displacement and mechanical resonance to be electrically detected. The cantilever fabricated on (0 0 1) substrate showed much smaller quality factors, indicating it has much larger energy dissipation than the one on (1 1 1) A. The measurement of the temperature dependence of the elastic constant suggests increased unharmonic lattice vibration for the (0 0 1) sample. These differences between (1 1 1) A and (0 0 1) samples could be induced by the high density of misfit dislocations formed in the (0 0 1) heterostructures. # 2004 Elsevier B.V. All rights reserved. PACS: 62.20.-x; 68.60.Bs; 72.20.Fr Keywords: MEMS; InAs; (1 1 1) A; Piezoresistance
1. Introduction Micro- and nano-electromechanical systems (MEMS/NEMS) have the potential to bring about a revolution in the application of semiconductor finestructure devices, such as high-resolution actuators and sensors, and high-frequency signal processing components [1]. The use of compound semiconductors could provide devices with novel functionality by * Corresponding author. Tel.: +81 46 240 3475; fax: +81 46 240 4727. E-mail address: [email protected] (H. Yamaguchi).
allowing us to combine both optoelectrical and mechanical properties [2,3]. InAs-based MEMS/ NEMS systems have an additional advantage of structure-size reduction to a nanometer scale [4,5]. However, for InAs-based systems, there is no practical candidate for the insulating lattice-matched substrate for heteroepitaxy. If we use highly mismatched substrates like GaAs or InP, the formation of misfit dislocations will cause a large degradation of the mechanical properties. A solution to this problem is to use heteroepitaxial systems grown by molecular beam epitaxy (MBE) on (1 1 1) A substrates, where the growth of InAs pro-
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.06.128
650
H. Yamaguchi et al. / Applied Surface Science 237 (2004) 649–653
ceeds in a layer-by-layer mode despite the large lattice mismatch of 7% [6]. Releasing the lattice mismatch with confining the misfit dislocations at the heterointerface can grow InAs-based heterostructures with excellent crystalline quality [7]. We have already fabricated InAs/AlGaSb pieozresistive cantilevers and studied the dependence of piezoresistance on the InAs thickness [5]. In this paper, we compare the piezoreistive and mechanical properties of InAs/ ˚ subAl0.5Ga0.5Sb cantilevers on (111) and (001) A strates. The heterostructures grown on (001) substrate, which contains a high density of threading dislocations, are found to have much degraded mechanical resonance characteristics and large unharmonicity in the lattice vibrations.
2. Results and discussions An InAs (15 nm)/Al0.5Ga0.5Sb (285 nm) single heterostructure (SH) was grown on a GaAs (1 1 1) A substrate (sample (1 1 1) A-SH) and a Al0.5Ga0.5Sb (15 nm)/InAs (15 nm)/Al0.5Ga0.5Sb (670 nm) double heterostructures (DH) was grown on GaAs (1 1 1) A ((1 1 1) A-DH) and (0 0 1) ((0 0 1)-DH) substrates by MBE. As we have already mentioned, the use of a (1 1 1) A-oriented substrate allows the growth of highquality InAs and AlGaSb layers directly on the GaAs [5–7]. The carrier concentration and mobility at room temperature are shown in Table 1. After growth, the heteroepitaxial film was processed into a freestanding suspended structure by using a microfabrication technique [5]. A square cantilever pad with the length and width of 10 and 14 mm, respectively, is suspended by two 10 mm-long and 4 mm-wide supports (Fig. 1), Table 1 Sheet carrier concentration (Ns), electron mobility (m), displacement sensitivity, minimum detectable displacement (MDD), resonance frequency (fres), and quality factor (Q) measured for the three samplesa (1 1 1) A-SH (1 1 1) A-DH (0 0 1)-DH 12
2
Ns (10 cm ) 2.4 m (cm2/V s) 5,000 Sensitivity (106 nm1) 6.4 pffiffiffiffiffiffiffi 0.16 MDD (nm/ HZ) 278.2 fres (kHz) Q 1918 a
1.7 22,000 0.56 0.76 615.5 2123
All the data was obtained at 300 K.
0.92 25,000 6.8 0.13 707.4 447
which lead a current between two deposited AuGeNi Ohmic contacts through the cantilever pad. As the InAs layer is located at the surface side of the cantilever, the deflection induces a stain and a resistance change, i.e. piezoresistance, in the InAs thin film, making it possible to detect the cantilever displacement electrically. To characterize the sensitivity at room temperature, we induced cantilever deflection by AFM z-scanner modulation as the tip approached the cantilever apex while measuring the resistance change [5]. Table 1 also compares the sensitivity (dR/R/dz) and the minimum detectable displacement (MDD), i.e. the resistance change per unit displacement and the noise density divided by the sensitivity, respectively, at 1 kHz. The comparison of (1 1 1) A-SH and -DH samples demonstrates the importance of the Fermi level pinning at the InAs surface, which occurs only in the SH sample, in increasing the sensitivity. The effects of the piezoelectric field and deformation potential will modify the band structure of InAs thin film. On the other hand, the effects do not largely change the pinning position of Fermi level because the pinning position is determined by the local electronic states. Therefore, the modification significantly changes the carrier concentration and mobility because they depend on the relative position of Fermi level to the band structure. In contrast, the change in the band structure induced by the strain is expected to be smaller in the InAs well of DH structure. This is because the Fermi level is pinned only at the surface of Al0.5Ga0.5Sb cap layer and the Fermi level in InAs well is also modified by the strain in the same way as the band structure, leading to smaller piezoresistance than (1 1 1) A-SH. The comparison between (1 1 1) A-DH and (0 0 1)DH provides information about the effect of the piezoelectric field. The stress induced by the cantilever deflection is uniaxial along the cantilever length direction, creating a strain component perpendicular to the cantilever surface through the Poisson ratio. This strain component modifies the perpendicular electric field in the InAs well through the piezoelectric effect only for (1 1 1) A-DH because there is no piezoelectric effect in the (0 0 1) direction. The smaller piezoresistance of (1 1 1) A-DH than (0 0 1)-DH suggests that the effect of piezoelectric potential cancels the sum of other effects, such as deformation potential, in (1 1 1) A-DH.
H. Yamaguchi et al. / Applied Surface Science 237 (2004) 649–653
651
Fig. 1. A fabricated InAs/AlGaSb piezoresistive cantilever.
This piezoresistance transfers the mechanical displacement into resistance change, allowing the electrical characterization of the mechanical resonance of cantilevers. The sample were mounted on a piezoelectric actuator and mechanically driven by applying alternate voltage on the actuator. The mounted sample was placed in a vacuum chamber and the change in two-terminal resistance was measured as a function of drive frequency [8]. Fig. 2 shows the resistance change as a function of drive frequency measured at room temperature. We clearly observed the mechanical resonance of the cantilevers. The resonance frequency fres of a suspended cantilever beam with the length l and the thickness t is given by: fres
Ct ¼ 2 l
rffiffiffiffi E ; r
process probably made a difference in the cantilever size, resulting in the difference also in the resonance frequency (615.5 and 707.4 kHz for (1 1 1) A-DH and (0 0 1)-DH, respectively). The reason of lower resonance frequency of (1 1 1) A-SH is the smaller canti-
(1)
where C is a constant of the order of unity, E Young’s modulus in the direction of cantilever length, and r the density. As the cantilever length direction was chosen to be ½110 for the (1 1 1) A and (0 0 1) samples, E should have the same value for both. Although the designed cantilever size was identical for (1 1 1) ADH and (0 0 1)-DH, difference in the details of etching
Fig. 2. Measured resistance change as a function of actuation frequency for the three fabricated samples.
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H. Yamaguchi et al. / Applied Surface Science 237 (2004) 649–653
lever thickness than other two samples. The results are summarized also in Table 1. The comparison of the quality factor (Q) confirms the large degradation of crystalline quality of (0 0 1)DH samples. On GaAs (0 0 1) substrates, the deposition of InAs (and also AlGaSb) shows Stranski Krastanov growth, and the overgrowth induced high-density of threading dislocations. In contrast, the InAs (and AlGaSb) layer grows in layer-by-layer fashion on (1 1 1) A surfaces and the misfit dislocations are confined at the interface with GaAs, allowing the growth of high crystalline quality heterostructures. The much larger Q for the (1 1 1) A-based structure is caused by the peculiar crystalline quality of (1 1 1) A-based structures. Low-temperature mechanical resonance characteristics were then measured for (1 1 1)A-DH and (0 0 1)-DH samples in a liquid helium cryostat. Fig. 3 shows the temperature dependence of the measured Q and resonance frequency. Q increased with decreasing temperature, indicating the drastic
suppression of internal friction at lower temperatures. We confirmed again the larger difference in Q between the two samples for the whole temperature range, where the ratio is rather more enhanced at low temperature. We also confirmed the shift in the resonance frequency with temperature [Fig. 3(b)]. The frequency shift is mainly caused by the change in the elastic constant. The temperature dependence of elastic constant Cij ((i, j) = (1, 1), (1, 2) or (4, 4)) has been reported to have the following form [9]: T Cij ðTÞ ¼ Cij0 1 Kij F ; (2) QDebye where Cij0 and Kij are constants, QDebye is the Debye temperature, and the function F(x) is given by: FðxÞ ¼ 3x4
Z
1=x
h3 ðeh 1Þ1 dh:
(3)
0
The relation between Young’s modulus E and Cij includes only the direction cosine of the cantilever
Fig. 3. Measured (a) quality factor and (b) resonance frequency as a function of temperature. The frequency was normalized by the value extrapolated to 0 K. The dotted line indicates the calculation using Eq. (2).
H. Yamaguchi et al. / Applied Surface Science 237 (2004) 649–653
as the other parameter [10], which is identical for the two samples. Therefore, we expected that both samples would have the same fractional variation in the resonance frequencies as a function of temperature. Our experimental result shows a discrepancy from this expectation, i.e. the elastic constant changes more ˚ . The dashed line in rapidly for (001) than (111) A Fig. 3(b) shows the variation calculated from Eq. (2). We used the average of reported values for GaSb and AlSb except for Kij because the values of Kij have not been reported for either AlGaSb or AlSb but only for GaSb [9]. We have also taken into account the small temperature dependence of r and the cantilever size, although the dependence gives only minority contributions. Compared with (1 1 1)A-DH, which agrees relatively well with the calculation, (0 0 1)-DH shows much stronger dependence on temperature. The temperature dependence of elastic constant is caused by the unharmonicity in the total crystal energy with respect to the lattice deformation [11]. The coupling of lattice mechanical deformation with the thermal vibration through the unharmonic part induced the reduced elastic constant at finite temperatures. The presence of dislocations in (0 0 1)-DH sample may be responsible for the additional unharmonicity because they could reduce the lattice stability and thereby decrease the elastic constant with large lattice deformation.
3. Conclusion In conclusion, we have compared the piezoresistance and the mechanical properties of piezoresistive
653
cantilevers fabricated from InAs/AlGaSb heterostructures. The quality factor in the mechanical resonance characteristics was significantly degraded for a (0 0 1)-based sample, suggesting enhanced energy dissipation by the misfit dislocations. The temperature dependence of the elastic constant was also measured and was found to increase unharmonicity, which was probably also induced by the threading dislocations.
Acknowledgement This work was supported by NEDO International Joint Research Program, ‘‘nano-elasticity’’.
References [1] H.G. Craighead, Science 290 (2000) 1532. [2] Y. Uenishi, H. Tanaka, H. Ukita, IEICE Trans. Electron. E78-C (2) (1995) 139. [3] R.G. Beck, M.A. Eriksson, M.A. Topinka, R.M. Westervelt, K.D. Maranowski, A.C. Gossard, Appl. Phys. Lett. 73 (1998) 1149. [4] H. Yamaguchi, Y. Hirayama, Appl. Phys. Lett. 80 (2002) 4428. [5] H. Yamaguchi, S. Miyashita, Y. Hirayama, Appl. Phys. Lett. 82 (2003) 394. [6] H. Yamaguchi, M.R. Fahy, B.A. Joyce, Appl. Phys. Lett. 69 (1996) 776. [7] H. Yamaguchi, J.G. Belk, X.M. Zhang, J.L. Sudijono, M.R. Fahy, T.S. Jones, D.W. Pashley, B.A. Joyce, Phys. Rev. B 55 (1997) 1337. [8] H. Yamaguchi, S. Miyashita, Y. Hirayama, Physica E, in press. [9] W.F. Boyle, R.J. Sladek, Phys. Rev. B 11 (1975) 2933. [10] W.A. Brantley, J. Appl. Phys. 44 (1973) 534. [11] G. Leibfried, W. Ludwig, Solid State Physics, Academic Press, New York, 1961.
Mechanical and piezoresistive properties of InAs/AlGaSb cantilevers H. Yamaguchia,*, S. Miyashitab, Y. Hirayamaa,c a
NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198, Japan b NTT Advanced Technology, Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan c Core Research for Evolutional Science and Technology (CREST), JST, Japan Available online 4 August 2004
Abstract We fabricated piezoresistive micromechanical cantilevers using InAs/AlGaSb heterostructures grown by molecular beam epitaxy on GaAs (1 1 1) A and (0 0 1) substrates. The piezoresistance allows the cantilever displacement and mechanical resonance to be electrically detected. The cantilever fabricated on (0 0 1) substrate showed much smaller quality factors, indicating it has much larger energy dissipation than the one on (1 1 1) A. The measurement of the temperature dependence of the elastic constant suggests increased unharmonic lattice vibration for the (0 0 1) sample. These differences between (1 1 1) A and (0 0 1) samples could be induced by the high density of misfit dislocations formed in the (0 0 1) heterostructures. # 2004 Elsevier B.V. All rights reserved. PACS: 62.20.-x; 68.60.Bs; 72.20.Fr Keywords: MEMS; InAs; (1 1 1) A; Piezoresistance
1. Introduction Micro- and nano-electromechanical systems (MEMS/NEMS) have the potential to bring about a revolution in the application of semiconductor finestructure devices, such as high-resolution actuators and sensors, and high-frequency signal processing components [1]. The use of compound semiconductors could provide devices with novel functionality by * Corresponding author. Tel.: +81 46 240 3475; fax: +81 46 240 4727. E-mail address: [email protected] (H. Yamaguchi).
allowing us to combine both optoelectrical and mechanical properties [2,3]. InAs-based MEMS/ NEMS systems have an additional advantage of structure-size reduction to a nanometer scale [4,5]. However, for InAs-based systems, there is no practical candidate for the insulating lattice-matched substrate for heteroepitaxy. If we use highly mismatched substrates like GaAs or InP, the formation of misfit dislocations will cause a large degradation of the mechanical properties. A solution to this problem is to use heteroepitaxial systems grown by molecular beam epitaxy (MBE) on (1 1 1) A substrates, where the growth of InAs pro-
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.06.128
650
H. Yamaguchi et al. / Applied Surface Science 237 (2004) 649–653
ceeds in a layer-by-layer mode despite the large lattice mismatch of 7% [6]. Releasing the lattice mismatch with confining the misfit dislocations at the heterointerface can grow InAs-based heterostructures with excellent crystalline quality [7]. We have already fabricated InAs/AlGaSb pieozresistive cantilevers and studied the dependence of piezoresistance on the InAs thickness [5]. In this paper, we compare the piezoreistive and mechanical properties of InAs/ ˚ subAl0.5Ga0.5Sb cantilevers on (111) and (001) A strates. The heterostructures grown on (001) substrate, which contains a high density of threading dislocations, are found to have much degraded mechanical resonance characteristics and large unharmonicity in the lattice vibrations.
2. Results and discussions An InAs (15 nm)/Al0.5Ga0.5Sb (285 nm) single heterostructure (SH) was grown on a GaAs (1 1 1) A substrate (sample (1 1 1) A-SH) and a Al0.5Ga0.5Sb (15 nm)/InAs (15 nm)/Al0.5Ga0.5Sb (670 nm) double heterostructures (DH) was grown on GaAs (1 1 1) A ((1 1 1) A-DH) and (0 0 1) ((0 0 1)-DH) substrates by MBE. As we have already mentioned, the use of a (1 1 1) A-oriented substrate allows the growth of highquality InAs and AlGaSb layers directly on the GaAs [5–7]. The carrier concentration and mobility at room temperature are shown in Table 1. After growth, the heteroepitaxial film was processed into a freestanding suspended structure by using a microfabrication technique [5]. A square cantilever pad with the length and width of 10 and 14 mm, respectively, is suspended by two 10 mm-long and 4 mm-wide supports (Fig. 1), Table 1 Sheet carrier concentration (Ns), electron mobility (m), displacement sensitivity, minimum detectable displacement (MDD), resonance frequency (fres), and quality factor (Q) measured for the three samplesa (1 1 1) A-SH (1 1 1) A-DH (0 0 1)-DH 12
2
Ns (10 cm ) 2.4 m (cm2/V s) 5,000 Sensitivity (106 nm1) 6.4 pffiffiffiffiffiffiffi 0.16 MDD (nm/ HZ) 278.2 fres (kHz) Q 1918 a
1.7 22,000 0.56 0.76 615.5 2123
All the data was obtained at 300 K.
0.92 25,000 6.8 0.13 707.4 447
which lead a current between two deposited AuGeNi Ohmic contacts through the cantilever pad. As the InAs layer is located at the surface side of the cantilever, the deflection induces a stain and a resistance change, i.e. piezoresistance, in the InAs thin film, making it possible to detect the cantilever displacement electrically. To characterize the sensitivity at room temperature, we induced cantilever deflection by AFM z-scanner modulation as the tip approached the cantilever apex while measuring the resistance change [5]. Table 1 also compares the sensitivity (dR/R/dz) and the minimum detectable displacement (MDD), i.e. the resistance change per unit displacement and the noise density divided by the sensitivity, respectively, at 1 kHz. The comparison of (1 1 1) A-SH and -DH samples demonstrates the importance of the Fermi level pinning at the InAs surface, which occurs only in the SH sample, in increasing the sensitivity. The effects of the piezoelectric field and deformation potential will modify the band structure of InAs thin film. On the other hand, the effects do not largely change the pinning position of Fermi level because the pinning position is determined by the local electronic states. Therefore, the modification significantly changes the carrier concentration and mobility because they depend on the relative position of Fermi level to the band structure. In contrast, the change in the band structure induced by the strain is expected to be smaller in the InAs well of DH structure. This is because the Fermi level is pinned only at the surface of Al0.5Ga0.5Sb cap layer and the Fermi level in InAs well is also modified by the strain in the same way as the band structure, leading to smaller piezoresistance than (1 1 1) A-SH. The comparison between (1 1 1) A-DH and (0 0 1)DH provides information about the effect of the piezoelectric field. The stress induced by the cantilever deflection is uniaxial along the cantilever length direction, creating a strain component perpendicular to the cantilever surface through the Poisson ratio. This strain component modifies the perpendicular electric field in the InAs well through the piezoelectric effect only for (1 1 1) A-DH because there is no piezoelectric effect in the (0 0 1) direction. The smaller piezoresistance of (1 1 1) A-DH than (0 0 1)-DH suggests that the effect of piezoelectric potential cancels the sum of other effects, such as deformation potential, in (1 1 1) A-DH.
H. Yamaguchi et al. / Applied Surface Science 237 (2004) 649–653
651
Fig. 1. A fabricated InAs/AlGaSb piezoresistive cantilever.
This piezoresistance transfers the mechanical displacement into resistance change, allowing the electrical characterization of the mechanical resonance of cantilevers. The sample were mounted on a piezoelectric actuator and mechanically driven by applying alternate voltage on the actuator. The mounted sample was placed in a vacuum chamber and the change in two-terminal resistance was measured as a function of drive frequency [8]. Fig. 2 shows the resistance change as a function of drive frequency measured at room temperature. We clearly observed the mechanical resonance of the cantilevers. The resonance frequency fres of a suspended cantilever beam with the length l and the thickness t is given by: fres
Ct ¼ 2 l
rffiffiffiffi E ; r
process probably made a difference in the cantilever size, resulting in the difference also in the resonance frequency (615.5 and 707.4 kHz for (1 1 1) A-DH and (0 0 1)-DH, respectively). The reason of lower resonance frequency of (1 1 1) A-SH is the smaller canti-
(1)
where C is a constant of the order of unity, E Young’s modulus in the direction of cantilever length, and r the density. As the cantilever length direction was chosen to be ½110 for the (1 1 1) A and (0 0 1) samples, E should have the same value for both. Although the designed cantilever size was identical for (1 1 1) ADH and (0 0 1)-DH, difference in the details of etching
Fig. 2. Measured resistance change as a function of actuation frequency for the three fabricated samples.
652
H. Yamaguchi et al. / Applied Surface Science 237 (2004) 649–653
lever thickness than other two samples. The results are summarized also in Table 1. The comparison of the quality factor (Q) confirms the large degradation of crystalline quality of (0 0 1)DH samples. On GaAs (0 0 1) substrates, the deposition of InAs (and also AlGaSb) shows Stranski Krastanov growth, and the overgrowth induced high-density of threading dislocations. In contrast, the InAs (and AlGaSb) layer grows in layer-by-layer fashion on (1 1 1) A surfaces and the misfit dislocations are confined at the interface with GaAs, allowing the growth of high crystalline quality heterostructures. The much larger Q for the (1 1 1) A-based structure is caused by the peculiar crystalline quality of (1 1 1) A-based structures. Low-temperature mechanical resonance characteristics were then measured for (1 1 1)A-DH and (0 0 1)-DH samples in a liquid helium cryostat. Fig. 3 shows the temperature dependence of the measured Q and resonance frequency. Q increased with decreasing temperature, indicating the drastic
suppression of internal friction at lower temperatures. We confirmed again the larger difference in Q between the two samples for the whole temperature range, where the ratio is rather more enhanced at low temperature. We also confirmed the shift in the resonance frequency with temperature [Fig. 3(b)]. The frequency shift is mainly caused by the change in the elastic constant. The temperature dependence of elastic constant Cij ((i, j) = (1, 1), (1, 2) or (4, 4)) has been reported to have the following form [9]: T Cij ðTÞ ¼ Cij0 1 Kij F ; (2) QDebye where Cij0 and Kij are constants, QDebye is the Debye temperature, and the function F(x) is given by: FðxÞ ¼ 3x4
Z
1=x
h3 ðeh 1Þ1 dh:
(3)
0
The relation between Young’s modulus E and Cij includes only the direction cosine of the cantilever
Fig. 3. Measured (a) quality factor and (b) resonance frequency as a function of temperature. The frequency was normalized by the value extrapolated to 0 K. The dotted line indicates the calculation using Eq. (2).
H. Yamaguchi et al. / Applied Surface Science 237 (2004) 649–653
as the other parameter [10], which is identical for the two samples. Therefore, we expected that both samples would have the same fractional variation in the resonance frequencies as a function of temperature. Our experimental result shows a discrepancy from this expectation, i.e. the elastic constant changes more ˚ . The dashed line in rapidly for (001) than (111) A Fig. 3(b) shows the variation calculated from Eq. (2). We used the average of reported values for GaSb and AlSb except for Kij because the values of Kij have not been reported for either AlGaSb or AlSb but only for GaSb [9]. We have also taken into account the small temperature dependence of r and the cantilever size, although the dependence gives only minority contributions. Compared with (1 1 1)A-DH, which agrees relatively well with the calculation, (0 0 1)-DH shows much stronger dependence on temperature. The temperature dependence of elastic constant is caused by the unharmonicity in the total crystal energy with respect to the lattice deformation [11]. The coupling of lattice mechanical deformation with the thermal vibration through the unharmonic part induced the reduced elastic constant at finite temperatures. The presence of dislocations in (0 0 1)-DH sample may be responsible for the additional unharmonicity because they could reduce the lattice stability and thereby decrease the elastic constant with large lattice deformation.
3. Conclusion In conclusion, we have compared the piezoresistance and the mechanical properties of piezoresistive
653
cantilevers fabricated from InAs/AlGaSb heterostructures. The quality factor in the mechanical resonance characteristics was significantly degraded for a (0 0 1)-based sample, suggesting enhanced energy dissipation by the misfit dislocations. The temperature dependence of the elastic constant was also measured and was found to increase unharmonicity, which was probably also induced by the threading dislocations.
Acknowledgement This work was supported by NEDO International Joint Research Program, ‘‘nano-elasticity’’.
References [1] H.G. Craighead, Science 290 (2000) 1532. [2] Y. Uenishi, H. Tanaka, H. Ukita, IEICE Trans. Electron. E78-C (2) (1995) 139. [3] R.G. Beck, M.A. Eriksson, M.A. Topinka, R.M. Westervelt, K.D. Maranowski, A.C. Gossard, Appl. Phys. Lett. 73 (1998) 1149. [4] H. Yamaguchi, Y. Hirayama, Appl. Phys. Lett. 80 (2002) 4428. [5] H. Yamaguchi, S. Miyashita, Y. Hirayama, Appl. Phys. Lett. 82 (2003) 394. [6] H. Yamaguchi, M.R. Fahy, B.A. Joyce, Appl. Phys. Lett. 69 (1996) 776. [7] H. Yamaguchi, J.G. Belk, X.M. Zhang, J.L. Sudijono, M.R. Fahy, T.S. Jones, D.W. Pashley, B.A. Joyce, Phys. Rev. B 55 (1997) 1337. [8] H. Yamaguchi, S. Miyashita, Y. Hirayama, Physica E, in press. [9] W.F. Boyle, R.J. Sladek, Phys. Rev. B 11 (1975) 2933. [10] W.A. Brantley, J. Appl. Phys. 44 (1973) 534. [11] G. Leibfried, W. Ludwig, Solid State Physics, Academic Press, New York, 1961.