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Figures

Image of FIG. 1.

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FIG. 1.

Strain and electric field in a ZB AlN/GaN QW. Reprinted with permission from L. Duggen, M. Willatzen, and B. Lassen, Phys. Rev. B 78, 205323 (2008). ©2008, American Physical Society.

Image of FIG. 2.

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FIG. 2.

(a) Piezoelectric field as a function of In composition . Circles: calculations using DFT computed linear and nonlinear piezoelectric coefficients. Reprinted with permission from Ref. 2. (b) Piezoelectric coefficient as a function of In composition . Hollow squares (theory) are from Ref. 54, hollow circle from Ref. 70, upside-down triangles from Ref. 71, triangles from Ref. 72, star from Ref. 73, filled circles from Refs. 74–76. Reprinted with permission from M. A. Miglionato, D. Powell, A. G. Cullis, T. Hammerschmidt, and G. P. Srivastava, Phys. Rev. B 74, 245332 (2006). ©2006, American Physical Society.

Image of FIG. 3.

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FIG. 3.

Piezoelectric potential for dots. Reprinted with permission from J. H. Davies, J. Appl. Phys. 84, 1358 (1998). ©1998, American Institute of Physics..

Image of FIG. 4.

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FIG. 4.

AlN/GaN heterostructures. (a) Crystal structures. (b) Direction of piezoelectric (PE) and spontaneous (SP) polarizations. Reprinted with permission from O. Ambacher, B. Foutz, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, A. J. Sierakowski, W. J. Schaff, L. F. Eastman, R. Dimitrov, A. Mitchell, and M. Stutzmann, , J. Appl. Phys. 87, 334 (2000). ©2000, American Institute of Physics.

Image of FIG. 5.

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FIG. 5.

Schematics of the two-layer HFET structure. Reprinted with permission from M. Willatzen, B. Lassen, and L. C. Lew Yan Voon, J. Appl. Phys. 100, 124309 (2006). ©2006, American Institute of Physics.

Image of FIG. 6.

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FIG. 6.

Internal field for 3 nm QWs. Reprinted with permission from S.-H. Park and D. Ahn, Appl. Phys. Lett. 94, 083507 (2009). ©2009, American Institute of Physics.

Image of FIG. 7.

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FIG. 7.

(a) Electric field (filled circles—Ref. 106, open circles—Ref. 105) and (b) polarization and charge density , as a function of Cd concentration in QWs. Reprinted with permission from F. Benharrats, K. Zitouni, A. Kadri, and B. Gil, Superlattices Microstruct. 47, 592 (2010). ©2010, Elsevier.

Image of FIG. 8.

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FIG. 8.

Polarization field for InGaN/GaN QWs using two sets of material parameters. Reprinted with permission from M. Feneberg and K. Thonke, J. Phys.: Condens. Matter 19, 403201 (2007). ©2007, Institute of Physics.

Image of FIG. 9.

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FIG. 9.

Left: first rotation of angle around the -axis. Right: second rotation of angle around the intermediate -axis. The growth direction of the heterostructure is always chosen to be along the -direction such that the interface planes are coplanar with the -plane. Reprinted with permission from L. Duggen and M. Willatzen, Phys. Rev. B 82, 205303 (2010). ©2010, American Physical Society.

Image of FIG. 10.

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FIG. 10.

Compressional strain component in AlN for a GaN/AlN/GaN heterostructure; (a) the fully-coupled and the semicoupled models corresponding to and for (b) several applied electric displacement fields (in units of ). Reprinted with permission from L. Duggen and M. Willatzen, Phys. Rev. B 82, 205303 (2010). ©2010, American Physical Society.

Image of FIG. 11.

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FIG. 11.

Electric field component in AlN for a GaN/AlN/GaN heterostructure; (a) corresponding to and (b) for several applied electric displacements . The legend is the same as in Fig. 10. Reprinted with permission from L. Duggen and M. Willatzen, Phys. Rev. B 82, 205303 (2010). ©2010, American Physical Society.

Image of FIG. 12.

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FIG. 12.

Compressional strain component in the QW layer (ZnO/MgO/ZnO heterostructure) for (a) the fully-coupled and the semicoupled models corresponding to (in units of ) and for (b) several applied electric displacement fields . Reprinted with permission from L. Duggen and M. Willatzen, Phys. Rev. B 82, 205303 (2010). ©2010, American Physical Society.

Image of FIG. 13.

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FIG. 13.

Shear strain component in the QW layer (ZnO/MgO/ZnO heterostructure) for (a) the fully-coupled and the semicoupled models corresponding to and for (b) several applied electric displacement fields . The legend is the same as in Fig. 12. Reprinted with permission from L. Duggen and M. Willatzen, Phys. Rev. B 82, 205303 (2010). ©2010, American Physical Society.

Image of FIG. 14.

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FIG. 14.

Electric field component in ZnMgO for a ZnO/ZnMgO/ZnO heterostructure; (a) corresponding to and (b) for several applied electric displacements . The legend is the same as in Fig. 12. Reprinted with permission from L. Duggen and M. Willatzen, Phys. Rev. B 82, 205303 (2010). ©2010, American Physical Society.

Image of FIG. 15.

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FIG. 15.

Polarization fields for a core shell nanowire. Reprinted with permission from M. A. Mastro, B. Simpkins, G. T. Wang, J. Hite, C. R. Eddy, Jr., H.-Y. Kim, J. Ahn, and J. Kim, Nanotechnology 21, 145205 (2010). ©2010, Institute of Physics.

Image of FIG. 16.

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FIG. 16.

Comparison between a truncated cone and a hexagonal pyramid QD. Reprinted with permission from D. P. Williams, A. D. Andreev, E. P. O'Reilly, and D. A. Faux, Phys. Rev. B 72, 235318 (2005). ©2005, American Physical Society.

Image of FIG. 17.

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FIG. 17.

Comparison of contributions to the piezoelectric potential between GaN/AlN and InN/GaN QDs. Reprinted with permission from D. P. Williams, A. D. Andreev, E. P. O'Reilly, and D. A. Faux, Phys. Rev. B 72, 235318 (2005). ©2005, American Physical Society.

Image of FIG. 18.

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FIG. 18.

Piezoelectric potential for InAs/InP QDs (truncated cylindrical pyramids) on two different substrate orientations. Reprinted with permission from C. Cornet, A. Schliwa, J. Even, F. Doré, C. Celebi, A. Létoublon, E. Macé, C. Paranthoën, A. Simon, P. M. Koenraad, N. Bertru, D. Bimberg, and S. Loualiche, Phys. Rev. B 77, 035312 (2006). ©2006, American Physical Society.

Image of FIG. 19.

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FIG. 19.

-axis strain calculated using fully-coupled (solid lines) and semicoupled (dashed lines) models for as a function of the 2DEG concentration. Reprinted with permission from A. F. M. Anwar, R. T. Webster, and K. V. Smith, Appl. Phys. Lett. 88, 203510 (2006). ©2006, American Institute of Physics.

Image of FIG. 20.

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FIG. 20.

Plot of the AlN electric field vs the AlN layer thickness for an AlN film on GaN. The (a) solid, (b) dashed-dotted, (c) long-dashed, and (d) short-dashed curves correspond to employing (a) a nonlinear permittivity without interface charges, (b) a linear permittivity without interface charges, (c) a nonlinear permittivity with interface charges, and (d) linear permittivity with interface charges. The linear model is obtained from the nonlinear model by setting the coefficients: . Short-circuit voltage conditions are imposed over the full structure. Reprinted with permission from M. Willatzen, B. Lassen, and L. C. Lew Yan Voon, J. Appl. Phys. 100, 124309 (2006). ©2006, American Institute of Physics.

Image of FIG. 21.

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FIG. 21.

Band diagram for an (0001) QW surrounded by -doped GaN barriers with a dopant concentration of . Reprinted with permission from Schubert and Schubert, Appl. Phys. Lett. 96, 131102 (2010). ©2010, American Institute of Physics.

Image of FIG. 22.

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FIG. 22.

Wave functions for a 5 nm QW. The curves are without (solid) and with (dotted) polarization fields. Reprinted with permission from J. Galczak, R. P. Sarzala, and W. Nakwaski, Physics E 25, 504 (2005). ©2005, Elsevier.

Image of FIG. 23.

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FIG. 23.

Transition energy for a 5 nm QW. The curves are without (solid) and with (dotted) polarization fields. Reprinted with permission from J. Galczak, R. P. Sarzala, and W. Nakwaski, Physica E 25, 504 (2005). ©2005, Elsevier.

Image of FIG. 24.

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FIG. 24.

Energy splitting of states for an InAs/GaAs QD. Reprinted with permission from G. Bester, A. Zunger, X. Wu, and D. Vanderbilt, Phys. Rev. B 74, 081305(R) (2006). ©2006, American Physical Society.

Image of FIG. 25.

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FIG. 25.

Comparison between InAs/GaAs and InAs/InP QDs. Plot is the 75% isodensity contour. Reprinted with permission from J. Even, F. Doré, C. Cornet, and L. Pedesseau, Phys. Rev. B 77, 085305 (2008). ©2008, American Physical Society.

Image of FIG. 26.

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FIG. 26.

Strain component for of the GaN/AlN QD. Reprinted with permission from B. Lassen, D. Barettin, M. Willatzen, and L. C. Le Yan Voon, Microelectron. J. 39, 1226 (2008). ©2008, Elsevier.

Image of FIG. 27.

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FIG. 27.

Transmission electron microscopy images and curves for bent ZnO nanowires. Reprinted with permission from K. H. Liu, P. Gao, Z. Xu, X. D. Bai, and E. G. Wang, Appl. Phys. Lett. 92, 213105 (2008). ©2008, American Institute of Physics.

Image of FIG. 28.

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FIG. 28.

Resistivity, electron concentration, and carrier mobility as a function of nanowire bending. Reprinted with permission from K. H. Liu, P. Gao, Z. Xu, X. D. Bai, and E. G. Wang, Appl. Phys. Lett. 92, 213105 (2008). ©2008, American Institute of Physics.

Image of FIG. 29.

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FIG. 29.

Voltage distribution for a bent nanowire. Reproduced, with permission from American Chemical Society, from Ref. 148.

Image of FIG. 30.

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FIG. 30.

Schematic of a SAW device. Interdigital metal electrodes are placed on the upper surface (gray-black stripes). Reprinted with permission from Y. Gao and Z. L. Wang, Nano Lett. 7, 2499 (2007). ©2007, American Chemical Society.

Image of FIG. 31.

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FIG. 31.

2D-section of the SAW-device (as modeled in COMSOL MULTIPHYSICS). Reprinted with permission from D. B. Carstensen, T. Amby-Christensen, M. Willatzen, and P. V. Santos, Technical Acoustics 19, 1 (2008). ©2008, Technical Acoustics.

Image of FIG. 32.

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FIG. 32.

Orientation angle sweep—at constant frequency (1.022 GHz) (-displacement). Reprinted with permission from D. B. Carstensen, T. Amby-Christensen, M. Willatzen, and P. V. Santos, Technical Acoustics 19, 1 (2008). ©2008, Technical Acoustics.

Image of FIG. 33.

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FIG. 33.

Rayleigh wave at the top surface , frequency equals 1.022 GHz (-displacement). Reprinted with permission from D. B. Carstensen, T. Amby-Christensen, M. Willatzen, and P. V. Santos, Technical Acoustics 19, 1 (2008). ©2008, Technical Acoustics.

Image of FIG. 34.

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FIG. 34.

Rayleigh wave at the top and bottom surfaces for . The frequency equals 1.022 GHz (-displacement). A similar mode is found at , however, characterized by a most significant displacement at the top surface. Reprinted with permission from D. B. Carstensen, T. Amby-Christensen, M. Willatzen, and P. V. Santos, Technical Acoustics 19, 1 (2008). ©2008, Technical Acoustics.

Image of FIG. 35.

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FIG. 35.

Rayleigh wave at the bottom surface corresponding to and the frequency equals 1.022 GHz (-displacement). Reprinted with permission from D. B. Carstensen, T. Amby-Christensen, M. Willatzen, and P. V. Santos, Technical Acoustics 19, 1 (2008). ©2008, Technical Acoustics.

Image of FIG. 36.

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FIG. 36.

Frequency sweep fixed angle (-displacement). Reprinted with permission from D. B. Carstensen, T. Amby-Christensen, M. Willatzen, and P. V. Santos, Technical Acoustics 19, 1 (2008). ©2008, Technical Acoustics.

Image of FIG. 37.

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FIG. 37.

Frequency sweep near 1.022 GHz for a fixed rotation angle: (-displacement). Reprinted with permission from D. B. Carstensen, T. Amby-Christensen, M. Willatzen, and P. V. Santos, Technical Acoustics 19, 1 (2008). ©2008, Technical Acoustics.

Image of FIG. 38.

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FIG. 38.

Lamb wave at a frequency of 1.512 GHz. The rotation angle is (-displacement). Reprinted with permission from D. B. Carstensen, T. Amby-Christensen, M. Willatzen, and P. V. Santos, Technical Acoustics 19, 1 (2008). ©2008, Technical Acoustics.

Tables

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Table I.

Representative values of piezoelectric coefficients and spontaneous polarization from the literature. is for the ZB structure and the rest is for the WZ structure. All data are taken from Bernardini et al. (Ref. 41) except for those of MgO and CdO taken from Gopal and Spaldin (Ref. 47).

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Table II.

Quadratic piezoelectric coefficients .

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Table III.

(in ) coefficients: calculated and experimental.

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Table IV.

Contributions to in the [111]-grown QW layer for different material compositions corresponding to open-circuit conditions. For , both and , being the theoretical and the experimental electric field in the QW layer, respectively, are listed for comparison.

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Table V.

Contributions to the vertical strain in a given layer. The material system: AlN/GaN means GaN is buffer or substrate while AlN is a thin film or QW.63,101

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Table VI.

Electron energies (eV) for a GaN/AlN QD. The zero of energy is the bulk GaN conduction-band edge. Reproduced with permission from Ref. 92.

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2011-02-09
2014-04-16

Abstract

Electromechanical phenomena in semiconductors are still poorly studied from a fundamental and an applied science perspective, even though significant strides have been made in the last decade or so. Indeed, most current electromechanical devices are based on ferroelectric oxides. Yet, the importance of the effect in certain semiconductors is being increasingly recognized. For instance, the magnitude of the electric field in an AlN/GaN nanostructure can reach 1–10 MV/cm. In fact, the basic functioning of an (0001) AlGaN/GaN high electron mobility transistor is due to the two-dimensional electron gas formed at the material interface by the polarization fields. The goal of this review is to inform the reader of some of the recent developments in the field for nanostructures and to point out still open questions. Examples of recent work that involves the piezoelectric and pyroelectric effects in semiconductors include: the study of the optoelectronic properties of III-nitrides quantum wells and dots, the current controversy regarding the importance of the nonlinear piezoelectric effect, energy harvesting using ZnO nanowires as a piezoelectric nanogenerator, the use of piezoelectric materials in surface acoustic wave devices, and the appropriateness of various models for analyzing electromechanical effects. Piezoelectric materials such as GaN and ZnO are gaining more and more importance for energy-related applications; examples include high-brightness light-emitting diodes for white lighting, high-electron mobility transistors, and nanogenerators. Indeed, it remains to be demonstrated whether these materials could be the ideal multifunctional materials. The solutions to these and other related problems will not only lead to a better understanding of the basic physics of these materials, but will validate new characterization tools, and advance the development of new and better devices. We will restrict ourselves to nanostructures in the current article even though the measurements and calculations of the bulk electromechanical coefficients remain challenging. Much of the literature has focused on InGaN/GaN, AlGaN/GaN, ZnMgO/ZnO, and ZnCdO/ZnO quantum wells, and InAs/GaAs and AlGaN/AlN quantum dots for their optoelectronic properties; and work on the bending of nanowires have been mostly for GaN and ZnO nanowires. We hope the present review article will stimulate further research into the field of electromechanical phenomena and help in the development of applications.

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Scitation: Electromechanical phenomena in semiconductor nanostructures
http://aip.metastore.ingenta.com/content/aip/journal/jap/109/3/10.1063/1.3533402
10.1063/1.3533402
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