Skip to main content

The Few-Body Problem in Nanoelectronics

  • Chapter
Granular Nanoelectronics

Part of the book series: NATO ASI Series ((NSSB,volume 251))

  • 309 Accesses

Abstract

Few electron systems are achieved by constraining electron motion so that one is no longer dealing with macroscopic bulk matter. (Similar remarks clearly apply to holes, which will be discussed specifically in our remarks on excitons). The constraints are effectively potential barriers which facilitate the creation of low-dimensional (d = 2, 1 or 0) systems. The zero-dimensional systems are the archetype of few electron systems but few electron aspects also play an important role in all low-d-systems. However, since d = 3 (bulk matter) and d = 2 (quantum well, semiconductor-insulator interface) systems have been extensively reviewed in the recent literature our emphasis will be on d = 1 (quantum wires) and d = 0 (quantum dots or boxes). We will concentrate on transport and noise properties but, in the case d = 0, we will also review other topics such as magnetic susceptibility, energy levels etc.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Al’tshuler, B. L. and Lee, P. A., 1988, Disordered Electronic Systems, Phys. To-Day, 41(12): 36.

    ADS  Google Scholar 

  • Brinkop, F., Hansen, W., Kotthaus, J. P. and Ploog, K., 1988, One-dimensional Subbands of Narrow Electron Channels in Gated AlxGa1-x As/GaAs Heterojunctions, Phys. Rev. B, 37: 6547.

    Article  ADS  Google Scholar 

  • Bryant, G. W., 1984, Hydrogenic Impurity States in Quantum-Well Wires, Phys. Rev. B, 29: 6632.

    Article  ADS  Google Scholar 

  • Bryant, G. W., 1985, Hydrogenic Impurity States in Quantum-Well Wires: Shape Effects, Phys. Rev. B, 31: 7812.

    Article  ADS  Google Scholar 

  • Bryant, G. W., 1987, Electronic Structure of Ultrasmali Quantum-Well Boxes, Phys. Rev. Lett., 59: 1140.

    Article  ADS  Google Scholar 

  • Bryant, G. W., 1988, Excitons in Quantum Boxes: Correlation Effects and Quantum Confinement, Phys. Rev. B, 37: 8763.

    Article  ADS  Google Scholar 

  • Callen, H. B. and Welton, T. A., 1951, Irreversibility and Generalized Noise, Phys. Rev., 83: 34.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Das Sarma, S. and Lai, W. Y., 1985, Screening and Elementary Excitations in Narrow — Channel Semiconductor Microstructures, Phys. Rev. B, 32: 1401.

    Article  ADS  Google Scholar 

  • Demel, T., Heitmann, D., Grambow, P. and Plogg, K., 1988, Far-infrared Response of One-Dimensional Electronic Systems in Single- and Two-layered Quantum Wires, Phys. Rev.B, 38: 12732.

    Article  ADS  Google Scholar 

  • Farmer, K. R., Rogers, C. T. and Buhrman, R. A., 1987, Localized-State Interactions in Metal-Oxide-Semiconductor Tunnel Diodes, Phys. Rev. Lett., 58: 2255.

    Article  ADS  Google Scholar 

  • Feng, S., Lee, P. A. and Stone, A. D., 1986, Sensitivity of the Conductance of a Disordered Metal to the Motion of a Single Atom: Implications for 1/f Noise, Phys. Rev. Lett., 56; 1960, 2772(E).

    Article  ADS  Google Scholar 

  • Ford, G. W., Lewis, J. T. and O’Connell, R. F., 1988a, Quantum Langevin Equation, Phys. Rev. A, 37: 4419.

    Article  MathSciNet  ADS  Google Scholar 

  • Ford, G. W., Lewis, J. T. and O’Connell, R. F., 1988b, Quantum Oscillator in a Blackbody Radiation Field II. Direct Calculation of the Energy Using the Fluctuation-Dissipation Theorem, Annals. of Phys. (N. Y.), 185: 270, Eq. (A.14).

    Article  MathSciNet  ADS  Google Scholar 

  • Götze, W. and Wölfle, P., 1972, Homogeneous Dynamical Conductivity of Simple Metals, Phys. Rev.B, 6: 1226.

    Article  ADS  Google Scholar 

  • Hansen, W., Smith, T. P., Lee, K. Y., Brum, J. A., Knoedler, C. M., Hong, J. M. and Kern, D. P., 1989, Zeeman Bifurcation of Quantum-Dot Spectra, Phys. Rev. Lett., 62: 2168.

    Article  ADS  Google Scholar 

  • Hansen, W., Smith, T. P. and Lee, K. Y., 1990, Reply to Comment by Silsbee et al. (1990), Phys. Rev. Lett., 64: 1992.

    Article  ADS  Google Scholar 

  • Hayashi, C., 1987, Ultrafine Particles, Phys. To-Day, 40(12): 44.

    ADS  Google Scholar 

  • Hiramoto, T., 1988, The Quantum Interference Effect of Electron Waves in Semiconductor Quantum Wires Fabricated by Focused Ion Beam Implantation, Ph.D. Thesis, Tokyo University, unpublished.

    Google Scholar 

  • Hiramoto, T., Hirakawa, K., Iye, Y. and Ikoma, T., 1989, Phase Coherence Length of Electron Waves in Narrow AlGaAs/GaAs Quantum Wires Fabricated by Focused Ion Beam Implantation, Appl. Phys. Lett., 54: 2103.

    Article  ADS  Google Scholar 

  • Howard, R. E., Jackel, L. D., Mankiewich, P. M. and Skocpol, W. J., 1986, Electrons in Silicon Microstructures, Science, 231: 346.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1987, Quantum Transport for a Many-Body System Using a Quantum Langevin-Equation Approach, Phys. Rev. B, 36: 5798.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1988a, Quantum Theory of Transient Transport in a High Electric Field, Phys. Rev. B, 38: 1721.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1988b, A Theory of High Electric Field Transport, Physica, 149A: 1.

    Article  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1988c, Strong Electric Field Effect on Weak Localization, Physica, 153A: 114.

    Article  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1989a, Fluctuation Effects on the Cyclotron Resonance Spectrum for a Two-Dimensional Electron Gas, Phys. Rev. B, 37: 10391.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1989b, Cyclotron Resonance in Two-Dimensional Electron-Phonon-Impurity Systems and Applications to Si Metal-Oxide-Semiconductor Systems, Phys. Rev. B, 40: 11701.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1989c, Generalized Quantum Langevin Equations for High-Electric-Field Transport, Phys. Rev. B, 39: 12717.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1989d, Electric Field Effect on Weak Localization in a Semiconductor Quantum Wire, Solid-State Electron., 32: 1253.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1990a, 1/f Noise: A Nonlinear-Generalized-Langevin-Equation Approach, Phys. Rev. B, 41: 5586.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1990b, Weak Localization Theory for Lightly Doped Semiconductor Quantum Wires, J. Phys. Cond. Matter, 2: 5335.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1990c, Electron-Electron Interactions in Quasi-One-Dimensional Electron Systems, Phys. Rev. B, 42: 1290.

    Article  ADS  Google Scholar 

  • Hu, G. Y. and O’Connell, R. F., 1990d, Dielectric Response of a Quasi-One-Dimensional Electron System, J. Phys. Cond. Matter, in press.

    Google Scholar 

  • Huang, K., 1987, “Statistical Mechanics,” 2nd ed., (Wiley), p. 90.

    MATH  Google Scholar 

  • Ismail, K., Antoniadis, D. A. and Smith, H. I., 1989, One-Dimensional Subbands and Mobility Modulation in GaAs/AlGaAs Quantum Wires, Appl. Phys. Lett., 54: 1130.

    Article  ADS  Google Scholar 

  • Kash, K., Scherer, A., Worlock, J. M., Craighead, H. G. and Tamargo, M. C., 1986, Optical Spectroscopy of Ultrasmall Structures Etched from Quantum Wells, Appl. Phys. Lett., 49: 1043.

    Article  ADS  Google Scholar 

  • Khaikin, M. S., 1969, Magnetic Surface Levels, Adv. Phys., 18: 1.

    Article  ADS  Google Scholar 

  • Kouwenhoven, L. P., Hekking, F. W. J., van Wees, B. J., Harmans, C. J. P. M., Timmering, C. E., and Foxon, C. T., 1990, Transport Through a Finite One-Dimensional Crystal, Phys. Rev. Lett., 65: 361.

    Article  ADS  Google Scholar 

  • Landauer, R., 1970, Electrical Resistance of Disordered One-Dimensional Lattices, Phil. Mag., 21: 863.

    Article  ADS  Google Scholar 

  • Landauer, R., 1987, Electrical Transport in Open and Closed Systems, Z. Phys., B68: 217.

    Article  Google Scholar 

  • Landauer, R., 1989, Nanostructure Physics: Fashion or Depth?, in “Nanostructure Physics and Fabrication,” Reed, M. A. and Kirk, W. P., eds. (Academic Press).

    Google Scholar 

  • Lei, X. L. and Horing, N. J. M., 1989, Divergence in the Balance-Equation Theory of Resistivity, Phys. Rev. B, 40: 5985.

    Article  ADS  Google Scholar 

  • Li, Q. and Das Sarma, S., 1989, Collective Excitation Spectra of One-Dimensional Electron Systems, Phys. Rev. B, 40: 5860.

    Article  ADS  Google Scholar 

  • Lorke, A. and Kotthaus, J. P., 1990, Coupling of Quantum Dots on GaAs, Phys. Rev. Lett., 64: 2559.

    Article  ADS  Google Scholar 

  • Mahan, G. D., 1981, Many-Particle Physics, (Plenum Press). Re the Kubo formula, see pps. 192 and 222.

    Google Scholar 

  • Mori, H., 1965, Transport, Collective Motion, and Brownian Motion, Prog. Theor. Phys., 33: 423.

    Article  ADS  MATH  Google Scholar 

  • Mott, N. F. and Kaveh, M., 1981, The Conductivity of Disordered Systems and the Scaling Theory, J. Phys. C, 14: L659.

    Article  ADS  Google Scholar 

  • Mott, N. F. and Twose, W. D., 1961, The Theory of Impurity Conduction, Adv. Phys., 10: 107.

    Article  ADS  Google Scholar 

  • O’Connell, R. F., 1982, Two Dimensional Systems in Solid State and Surface Physics: Strong Electric and Magnetic Fields Effects, J. de Physique, Colloque C2: 81.

    Google Scholar 

  • Pepper, M., 1988, Quantum Processes in Semiconductor Structures, Proc. R. Soc. Lond., A420: 1.

    Article  ADS  Google Scholar 

  • Que, W. and Kirczenow, G., 1988, Theory of Collective Excitations in a Two-Dimensional Array of Quantum Dots, Phys. Rev. B, 38: 3614.

    Article  ADS  Google Scholar 

  • Ralph, D. C., Ralls, K. S. and Buhrman, R. A., 1989, Defect Motion, Electromigration and Conductance Fluctuations in Metal Nanocontacts, in “Nanostructure Physics and Fabrication, “ Reed, M. A., and Kirk, W. P., eds. (Academic Press).

    Google Scholar 

  • Reed, M. A., Randall, J. N., Aggarwal, R. J., Matyi, R. J., Moore, T. M. and Wetsel, A. E., 1988, Observation of Discrete Electronic States in a Zero-Dimensional Semiconductor Nanostructure, Phys. Rev. Lett., 60: 535.

    Article  ADS  Google Scholar 

  • Ralls, K. S., Skocpol, W. J., Jackel, L. D., Howard, R. E., Fetter, L. A., Epworth, R. W., and Tennant, D. M., 1984, Discrete Resistance Switching in Submicrometer Silicon Inversion Layers: Individual Interface Traps and Low-Frequency (1/f?) Noise, Phys. Rev. Lett., 52: 228.

    Article  ADS  Google Scholar 

  • Ralls, K. S. and Buhrman, R. A., 1988, Defect Interactions and Noise in Metallic Nanoconstrictions, Phys. Rev. Lett., 60: 2434.

    Article  ADS  Google Scholar 

  • Robnik, M., 1986, Perimeter Corrections to the Landau Diamagnetism, J. Phys. A., 19: 3619.

    Article  ADS  Google Scholar 

  • Rogers, C. T. and Buhrman, R. A., 1985, Nature of Single-Localized-Electron States Derived from Tunneling Measurements, Phys. Rev. Lett., 55: 859.

    Article  ADS  Google Scholar 

  • Sikorski, C. and Merkt, U., 1989, Spectroscopy of Electronic States in InSb Quantum Dots, Phys. Rev. Lett., 62: 2164.

    Article  ADS  Google Scholar 

  • Silsbee, R. H. and Ashoori, R. C., 1990, Comment on “Zeeman Bifurcation of Quantum-Dot Spectra”, Phys. Rev. Lett., 64: 1991.

    Article  ADS  Google Scholar 

  • Sivan, U., and Imry, Y., 1988, de Haas-van Alphen and Aharonov-Bohm-type Persistent Current Oscillations in Singly Connected Quantum Dots, Phys. Rev. Lett., 61: 1001.

    Article  ADS  Google Scholar 

  • Skocpol, W. J., Jackel, L. D., Hu, E. L., Howard, R. E., and Fetter, L. A., 1982, One-Dimensional Localization and Interaction Effects in Narrow (0.1-mm) Silicon Inversion Layers, Phys. Rev. Lett., 49: 951.

    Article  ADS  Google Scholar 

  • Skocpol, W. J., Mankiewich, P. M., Howard, R. E., Jackel, L. D., Tennant, D. M. and Stone, A. D., 1986, Universal Conductance Fluctuations in Silicon Inversion-Layer Nanostructures, Phys. Rev. Lett., 56: 2865.

    Article  ADS  Google Scholar 

  • Smith, T. P., Lee, K. Y., Knoedler, C. M., Hong, J. M. and Kern, D. P., 1988, Electronic Spectroscopy of Zero-Dimensional Systems, Phys. Rev. B 36: 2172.

    Article  ADS  Google Scholar 

  • Thouless, D. J., 1977, Maximum Metallic Resistance in Thin Wires, Phys. Rev. Lett., 39: 1167.

    Article  ADS  Google Scholar 

  • Thouless, D. J., 1980, The Effect of Inelastic Electron Scattering on the Conductivity of Very Thin Wires, Solid State Comm., 34: 683.

    Article  ADS  Google Scholar 

  • Uren, M. J., Day, D. J. and Kirton, M. J., 1985, 1/f and Random Telegraph Noise in Silicon Metal-Oxide-Semiconductor Field-Effect Transistors, Appl. Phys. Lett., 47: 1195.

    Article  ADS  Google Scholar 

  • Van Hove, L., 1957, The Approach to Equilibrium in Quantum Statistics: A Perturbation Treatment to General Order, Physica, 23: 441.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Van Wees, B. J., van Houten, H., Beenakker, C. W. J., Williamson, J. G., Kouwenhoven, L. P., and van der Marel, D., 1988, Quantized Conductance of Point Contacts in a Two-Dimensional Electron Gas, Phys. Rev. Lett., 60: 848.

    Article  ADS  Google Scholar 

  • Wang, L., and O’Connell, R. F., 1986, Surface Effects on the Diamagnetic Susceptibility and Other Properties of a Low-Temperature Electron Gas, Phys. Rev. B, 34: 5160.

    Article  ADS  Google Scholar 

  • Webb, R. A. and Washburn, S., Dec. 1988, Quantum Interference Fluctuations in Disordered Metals, Phys. To-Day, 41: 12, pps. 46–53.

    Google Scholar 

  • Wharam, D. A., Thornton, T. J., Newbury, R., Pepper, M., Ahmed, H., Frost, J. E. F., Hasko, D. G., Peacock, D. C., Ritchie, D. A., and Jones, G. A. C., 1988, One- Dimensional Transport and the Quantisation of the Ballistic Resistance, J. Phys. C, 21: L209.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

O’Connell, R.F., Hu, G.Y. (1991). The Few-Body Problem in Nanoelectronics. In: Ferry, D.K., Barker, J.R., Jacoboni, C. (eds) Granular Nanoelectronics. NATO ASI Series, vol 251. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3689-9_20

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-3689-9_20

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-3691-2

  • Online ISBN: 978-1-4899-3689-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics