Abstract
Recent advances in materials fabrication and nanolithography have made possible a generation of semiconducting structures whose conductance is governed by quantum mechanical phenomena. In particular, nanostructures on Si MOSFETs and GaAs MODFETs have shown modulations in their conductance versus gate voltage characteristics that have been attributed to quantum mechanical effects. In this paper, we review a modeling scheme which gives a unified way of understanding how these quantum effects are affected by temperature, mobility, voltage, and the structure of the device. This model provides not only a qualitative understanding of the various quantum phenomena, but also a basis for developing efficient computational algorithms for modeling specific devices. We have called this scheme the convolution method because most of the calculations can be written in terms of separate convolutions involving the individual phenomena of temperature, mobility, voltage, and structure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abrikosov, A. A., Gorkov, L. P., Dzyaloshinski, I. E., 1963, “Methods of Quantum Field Theory in Statistical Physics,” Prentice-Hall, Englewood Cliffs, N.J.
Al’tshuler, B. L., 1985, Fluctuations in the Extrinsic Conductivity of Disordered Conductors, Sov. Phys. JETP Lett., 41: 648.
Antoniadis, D. A., Warren, A. C., Smith, H. I., 1985, Quantum Mechanical Effects in Very Short and Very Narrow Channel MOSFETs, IEDM Tech. Dig., 562.
Ashcroft, N. W. Mermin, N. D., 1976, “Solid State Physics,” Holt, Rinehart, and Winston, New York.
Bagwell, P. F., 1988, “Quantum Mechanical Transport Phenomenon in Nano-structured Inversion Layers,” S. M. Thesis, MIT.
Bagwell, P. F., Antoniadis, D. A., Orlando, T. P., 1989, Quantum Mechanical and Non-Stationary Transport Phenomenon in Nanostructured Silicon Inversion Layers, in: “Advanced MOS Device Physics,” N. Einspruch and G. Gildenblat, ed., Academic Press, San Diego.
Bagwell, Phillip F., Orlando, Terry P., 1989a, Landauer’s Conductance Formula and its Generalization to Finite Voltages, Phys. Rev. B, 40: 1456.
Bagwell, P. F., Orlando, T. P., 1989b, Broadened Conductivity Tensor and Density of States for a Superlattice Potential in One, Two, and Three Dimensions, Phys. Rev. B, 40: 3735.
Bernstein, G., Ferry, D. K., 1987, Negative Differential Conductivity in Lateral Surface Superlattices, J. Vac. Sci. Technol. B, 5: 964.
Büttiker, M., Imry, Y., Landauer, R., Pinhas, S., 1985, Generalized Many-Channel Conductance Formula with Application to Small Rings, Phys. Rev. B, 31: 6207.
Büttiker, M., 1986, Role of Quantum Coherence in Resistors, Phys. Rev. B, 33:3020. See also Büttiker, M., 1988, Coherent and Sequential Tuneling in Series Barriers, IBM J. Res. Dev., 32: 63.
Fischer, Daniel S., Lee, Patrick A., 1981, Relation Between Conductivity and Transmission Matrix, Phys. Rev. B, 23: 6851.
Glazman, L. I., Khaetskii, A. V., 1988, Nonlinear Quantum Conductance of a Point Contact, JETP Lett., 48: 591.
Glazman, L. I., Khaetskii, A. V., 1989, Nonlinear Quantum Conductance of a Lateral Microconstraint in a Heterostructure, Europhys. Lett., 9: 263.
Ismail, K., Chu, W., Antoniadis, D. A., Smith, Henry I., 1988, Surface-Superlattice Effects in a Grating-Gate GaAs/GaAlAs Modulation-Doped Field- Effect-Transistor, Appl. Phys. Lett., 52: 1071.
Ismail, K., Chu, W., Yen, A., Antoniadis, D. A., Smith, Henry I., 1989a, Negative Transconductance and Negative Differential Resistance in a Grid-Gate Modulation Doped Field-Effect Transistor, Appl. Phys. Lett., 54: 460.
Ismail, K., Chu, W., Antoniadis, D. A., Smith, Henry I., 1989b, One Dimensional Subbands and Mobility Modulation in GaAs/AlGaAs Quantum Wires, Appl. Phys. Lett., 54: 1130.
Ismail, Khalid, 1989, “The Study of Electron Transport in Field-Induced Quantum Wells on GaAs/AlAs”, Ph. D. Thesis, MIT.
Kittel, C., 1986, “Introduction to Solid State Physics”, Wiley, New York.
Kouwenhoven, L. P., van Wees, B. J., Harmans, C. J. P. M., Williamson, J. G., van Houten, H., Beenakker, C. W. J., Foxon, C. T., Harris, J. J., 1989, Nonlinear Conductance of Quantum Point Contacts, Phys. Rev. 13., 39: 8040.
Landauer, R., 1957, Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction, IBM J. Res. Dev., 1: 223.
Landauer, Rolf, 1970, Electrical Resistance of Disordered One Dimensional Lattices, Phil. Mag., 21: 683.
Landauer, Rolf, 1987, Electrical Transport in Open and Closed Systems, Z. Phys. B., 68: 217.
Landauer, Rolf, 1989, Conductance Determined by Transmission: Probes and Quantized Constriction Resistance, to appear in J. Phys. Cond. Matt..
Lee, P. A., Stone, A. D., 1985, Universal Conductance Fluctuations in Metals, Phys. Rev. Lett., 55: 1622.
Madelung, O., 1978, “Introduction to Solid State Theory,” Springer-Verlag, New York.
Payne, M. C., 1989, Electrostatic and Electrochemical Potentials in Quantum Trans-port, J. Phys. Cond. Matt., 1: 4931.
Rickayzen, G., 1980, “Green’s Functions and Condensed Matter,” Academic Press, New York.
Scott-Thomas, J. H. F., Kastner, M. A., Antoniadis, D. A., Smith, Henry I., Field, Stuart, 1988, Si MOSFETs with 70nm Slotted Gates for Study of Quasi One Dimensional Quantum Transport, J. Vac. Set. Technol. B, 6: 1841.
Skocpol, W. J., Mankiewich, P. M., Howard, R. E., Jackel, L. D., Tennant, D. M., Stone, A. D., 1986, Universal Conductance Fluctuations in Silicon Inversion Layer Nanostructures, Phys. Rev. Lett., 56: 2865.
Tokura, Y., Tsubaki, K., 1987, Conductivity Oscillation due to Quantum Interference in a Proposed Washboard Transistor, Appl. Phys. Lett., 51: 1807.
van Wees, B. J., van Houten, H., Beenakker, C. W. J., Williamson, J. G., Kouwenhoven, L. P., van der Marel, D., Foxon, C. T., 1988, Quantized Conductance of Point Contacts in a Two Dimensional Electron Gas, Phys. Rev. Lett., 60: 848.
Warren, A. C., Antoniadis, D. A., Smith, H. I., Melngailis, J., 1985, Surface Superlattice Formation in Silicon Inversion Layers Using 0.2-/zm Period Grating-Gate Electrodes, IEEE Electron Dev. Lett., EDL-6: 294.
Warren, A. C., Antoniadis, D. A., Smith, H. I., 1986, Quasi One-Dimensional Conduction in Multiple, Parallel Inversion Lines, Phys. Rev. Lett., 56: 1858.
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., Jones, G. A. C., 1988, One Dimensional Transport and the Quantization of the Ballistic Resistance, J. Phys. C: Solid State Phys., 21: L209.
Wolf, E. L., 1985, “Principles of Electron Tunnelling Spectroscopy”, Oxford University Press, New York. See equations (2.5) and (2. 6 ).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Plenum Press, New York
About this chapter
Cite this chapter
Orlando, T.P., Bagwell, P.F., Ghanbari, R.A., Ismail, K. (1990). Quantum Device Modeling with the Convolution Method. In: Chamberlain, J.M., Eaves, L., Portal, JC. (eds) Electronic Properties of Multilayers and Low-Dimensional Semiconductor Structures. NATO ASI Series, vol 231. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7412-1_11
Download citation
DOI: https://doi.org/10.1007/978-1-4684-7412-1_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-7414-5
Online ISBN: 978-1-4684-7412-1
eBook Packages: Springer Book Archive