### Abstract

In a previous paper, we attempted to lay a conceptual framework for an ultimate physics of small semiconductor devices and concentrated on the medium small device. Here we treat the very small device (VSD), characterized by an effective channel length of 250 Å. We demonstrate how such a device could conceivably be fabricated using two side processing of the wafer. In treating the transport, however, it is found that the time and distance scales are such that the Boltzmann transport equation is completely invalidated. Here we develop the appropriate quantum transport equations based upon the density matrix for the entire system, device plus boundaries plus environment. It is found that the boundaries and environment can lead to renormalization of the energy spectrum as well as long range dissipative interactions. Two special cases of the transport equations are treated. If the transport is dominantly stochastic, an exact Langevin equation is found for the various transport parameters. In a second case, a parameterized density matrix is used in analogy to the displaced Maxwellian. In this latter case, a hierarchy of moment equations can be developed to yield, e.g. energy and momentum balance equations.

Original language | English (US) |
---|---|

Pages (from-to) | 531-544 |

Number of pages | 14 |

Journal | Solid State Electronics |

Volume | 23 |

Issue number | 6 |

DOIs | |

State | Published - 1980 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Solid State Electronics*,

*23*(6), 531-544. https://doi.org/10.1016/0038-1101(80)90034-9

**On the physics and modeling of small semiconductor devices-II. The very small device.** / Barker, J. R.; Ferry, D. K.

Research output: Contribution to journal › Article

*Solid State Electronics*, vol. 23, no. 6, pp. 531-544. https://doi.org/10.1016/0038-1101(80)90034-9

}

TY - JOUR

T1 - On the physics and modeling of small semiconductor devices-II. The very small device

AU - Barker, J. R.

AU - Ferry, D. K.

PY - 1980

Y1 - 1980

N2 - In a previous paper, we attempted to lay a conceptual framework for an ultimate physics of small semiconductor devices and concentrated on the medium small device. Here we treat the very small device (VSD), characterized by an effective channel length of 250 Å. We demonstrate how such a device could conceivably be fabricated using two side processing of the wafer. In treating the transport, however, it is found that the time and distance scales are such that the Boltzmann transport equation is completely invalidated. Here we develop the appropriate quantum transport equations based upon the density matrix for the entire system, device plus boundaries plus environment. It is found that the boundaries and environment can lead to renormalization of the energy spectrum as well as long range dissipative interactions. Two special cases of the transport equations are treated. If the transport is dominantly stochastic, an exact Langevin equation is found for the various transport parameters. In a second case, a parameterized density matrix is used in analogy to the displaced Maxwellian. In this latter case, a hierarchy of moment equations can be developed to yield, e.g. energy and momentum balance equations.

AB - In a previous paper, we attempted to lay a conceptual framework for an ultimate physics of small semiconductor devices and concentrated on the medium small device. Here we treat the very small device (VSD), characterized by an effective channel length of 250 Å. We demonstrate how such a device could conceivably be fabricated using two side processing of the wafer. In treating the transport, however, it is found that the time and distance scales are such that the Boltzmann transport equation is completely invalidated. Here we develop the appropriate quantum transport equations based upon the density matrix for the entire system, device plus boundaries plus environment. It is found that the boundaries and environment can lead to renormalization of the energy spectrum as well as long range dissipative interactions. Two special cases of the transport equations are treated. If the transport is dominantly stochastic, an exact Langevin equation is found for the various transport parameters. In a second case, a parameterized density matrix is used in analogy to the displaced Maxwellian. In this latter case, a hierarchy of moment equations can be developed to yield, e.g. energy and momentum balance equations.

UR - http://www.scopus.com/inward/record.url?scp=0019024582&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019024582&partnerID=8YFLogxK

U2 - 10.1016/0038-1101(80)90034-9

DO - 10.1016/0038-1101(80)90034-9

M3 - Article

VL - 23

SP - 531

EP - 544

JO - Solid-State Electronics

JF - Solid-State Electronics

SN - 0038-1101

IS - 6

ER -