Basic Semiconductor Physics.- Microscopic Semi-Classical Models.- Derivation of Macroscopic Equations.- Collisionless Models.- Scattering Models.- Macroscopic Semi-Classical Models.- Drift-Diffusion Equations.- Energy-Transport Equations.- Spherical Harmonics Expansion Equations.- Diffusive Higher-Order Moment Equations.- Hydrodynamic Equations.- Microscopic Quantum Models.- The Schr#x00F6 dinger Equation.- The Wigner Equation.- Macroscopic Quantum Models.- Quantum Drift-Diffusion Equations.- Quantum Diffusive Higher-Order Moment Equations.- Quantum Hydrodynamic Equations.

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Transport Equations for Semiconductors

This paper shows that various models of electron transport in semiconductors that have been previously proposed in the literature can be connected one with each other by the diffusion approximation methodology We first investigate the diffusion limit of the semiconductor Boltzmann equation towards the so‐called ‘‘spherical harmonic expansion model,’’ under the assumption of dominant elastic scattering Then, this model is again connected, either to the energy‐transport model or to a ‘‘periodic spherical harmonic expansion model’’ through a diffusion approximation, respectively making electron–electron or phonon scattering large We provide the mathematical background which makes the Hilbert expansions associated with these various diffusion limits rigorous

On a hierarchy of macroscopic models for semiconductors

Current flow, considering a semiclassical electron--electric-field interaction and electron scattering by acoustic phonons, is studied in semiconducting zig-zag carbon nanotubes. The $\ensuremath{\pi}$-electronic band structure and the phonon spectrum of the nanotube are both calculated from graphene by the zone-folding method. Scattering rates are calculated using first-order perturbation theory and the deformation-potential approximation, while the selection rules for the electron-phonon interaction are developed based on the conservation of crystal momentum. The steady-state transport properties of electrons in small-diameter nanotubes are simulated using the Monte Carlo method. Results show negative differential mobility occurring at smaller threshold fields as the tube diameter increases. The peak drift velocity is also found to depend on the tube diameter, and reaches values as high as $5\ifmmode\times\else\texttimes\fi{}{10}^{7}\mathrm{c}\mathrm{m}/\mathrm{s}$ in the largest tube considered with a diameter of $\ensuremath{\cong}4.6\mathrm{nm}.$ The simulated low-field mobility is as large as in graphite, $\ensuremath{\cong}2\ifmmode\times\else\texttimes\fi{}{10}^{4}{\mathrm{cm}}^{2}/\mathrm{V}/\mathrm{s},$ for the larger tubes, but decreases as the tube diameter decreases.

Semiclassical transport and phonon scattering of electrons in semiconducting carbon nanotubes

A light-absorbing layer is selectively formed over an insulating surface, an insulating layer is formed over the insulating surface and the light-absorbing layer, the insulating surface, the light-absorbing layer, and the insulating layer are irradiated with laser light to selectively remove only the insulating layer above the light-absorbing layer in an irradiated region of the insulating layer so that an opening reaching the light-absorbing layer is formed in the insulating layer, and a conductive film is formed in the opening so as to be in contact with the light-absorbing layer. By forming the conductive film in the opening so as to be in contact with the exposed light-absorbing layer, the conductive film can be electrically connected to the light-absorbing layer with the insulating layer interposed therebetween.

Method for manufacturing display device

Previous studies have demonstrated that lung volume during wakefulness influences upper airway size and resistance, particularly in patients with sleep apnea. We sought to determine the influence of lung volume on the level of continuous positive airway pressure (CPAP) required to prevent flow limitation during non-REM sleep in subjects with sleep apnea. Seventeen subjects (apnea–hypopnea index, 42.6 ± 6.2 [SEM]) were studied during stable non-REM sleep in a rigid head-out shell equipped with a positive/negative pressure attachment for manipulation of extrathoracic pressure. An epiglottic pressure catheter plus a mask/pneumotachometer were used to assess flow limitation. When lung volume was increased by 1,035 ± 22 ml, the CPAP level could be decreased from 11.9 ± 0.7 to 4.8 ± 0.7 cm H2O (p < 0.001) without flow limitation. The decreased CPAP at the same negative extrathoracic pressure yielded a final lung volume increase of 421 ± 36 ml above the initial value. Conversely, when lung volume was reduced by ...

Lung volume and continuous positive airway pressure requirements in obstructive sleep apnea

A computationally very efficient technique for obtaining the electron velocity distribution function in silicon is presented. Analytical methods using Legendre polynomials are combined with numerical techniques using matrices to solve the Boltzmann transport equation. Results agree with Monte Carlo calculations, but are obtained in approx. 1 100 the CPU time. The method accounts for the effects of acoustic and intervalley phonon scattering, as well as silicon's nonparabolic, ellipsoidal band structure. Accurate expressions for electron average energy, drift velocity and mobility in terms of the distribution function are also provided. The method is appropriate for use in CAD tools for semiconductor devices.

A physics-based analytical/numerical solution to the Boltzmann transport equation for use in device simulation

A method for calculating impact ionization coefficients by solving the Boltzmann transport equation is presented. The distribution function is taken to be expressible as a Legendre polynomial expansion, which is substituted into a Boltzmann equation that incorporates the effects of nonparabolic band structure, deformation‐potential phonon scattering, and impact ionization. The resulting Boltzmann equation can be expressed in a linear form, and solved using sparse‐matrix difference‐differential methods. Ionization coefficients are obtained directly from the distribution function. Calculated values for the ionization coefficients agree very well with experiment for electrons in silicon.

Efficient calculation of ionization coefficients in silicon from the energy distribution function

A new equation, which does not require any fitting parameters, has been developed to predict gate leakage current density in MOSFETs. The equation is based upon a non-Maxwellian hot-electron distribution function derived from the Boltzmann transport equation, and utilizes a physically calculated local electron temperature. The model predicts gate currents for a sample submicron MOSFET that are in good agreement with experiment.

Electron energy distribution for calculation of gate leakage current in MOSFETs

A method of continuous manufacture of semiconductor integrated circuits, said method and apparatus adapted to contain the semiconductor substrate, semiconductor deposition coating processes, and etching processes within a substantially collocated series of process chambers so that the semiconductor travels from one chamber to the next without exposure to airborne impurities and contact with manufacturing personnel. The invention has particular utility in the high volume fabrication of large surface area semiconductor circuits such as active matrix liquid crystal displays. The present invention contains a roll-to-roll and continuous belt embodiment.

Method for manufacturing semiconductor devices

The lucky-electron-exponential model (LE-EM) has been used with some success to model hot-electron-induced degradation. Examination of the LE-EM shows its exponential form is an approximation to the high-energy tails of Monte-Carlo-generated hot-electron distribution functions (HEDFs). It is also suggested that the proper LE-EM mean-free path lambda for use in calculating MOSFET gate leakage current is approximately 50 AA, while the commonly used value of 78 AA is appropriate for modeling phenomena related to impact ionization. >

Jeffrey Frey

Papers

A physics-based analytical/numerical solution to the Boltzmann transport equation for use in device simulation

Efficient calculation of ionization coefficients in silicon from the energy distribution function

Electron energy distribution for calculation of gate leakage current in MOSFETs

Method for manufacturing semiconductor devices

Reconciliation of a hot-electron distribution function with the lucky electron-exponential model in silicon