Drift velocity of electrons and holes and associated anisotropic effects in silicon

Publisher Summary This chapter deals with electron transport in crystals subjected to small driving forces, that is, low-field transport. It studies cases in which the driving forces are steady or time-dependent electric fields, or temperature gradients. It explores that extensive data have become available on many of the III–V and II–VI compounds. Because low-field transport coefficients are characteristic of microscopic properties of the crystals exclusive of the particular field strengths involved, detailed comparisons between theoretical and experimental results permit the construction of a generally satisfactory picture of the electron physics of these crystals. Recent improvements in transport calculations allow quantitative comparisons with experiments that are helpful in elucidating electron scattering mechanisms and in refining the knowledge of basic material constants. Naturally, these more accurate findings have dictated the elaboration of transport theory in a fashion consistent with band theory. Concerning electron–phonon scattering, there has been little hope in the past of determining the strength of a particular mechanism in the presence of other equally influential mechanisms. Extensions of some of the techniques to other materials, such as ternary and quaternary alloys, could greatly improve our quantitative understanding of the electron–phonon interaction.

Chapter 1 Low-Field Electron Transport

Scattering of charged particles is accompanied by the emission of soft photons. Handel's theory of 1/f noise, based on the infrared quasi-divergent coupling of the system to the electromagnetic field, indicates that the current associated with a beam of scattered particles will exhibit 1/f noise. His derivation is valid in a vacuum. Here we extend his results and obtain the fluctuation spectrum for the fluctuations in cross-section and for the scattering rates w kk′ in k-space, using the Born approximation. Next we consider mobility fluctuations due to these scattering rates, employing the relaxation time solutions of the Boltzmann transport equation, valid in non-degenerate semiconductors. Explicit results are obtained for the mobility-fluctuation noise caused by ionized impurity scattering, acoustic phonon scattering, optical phonon scattering, polar optical phonon scattering, and intervalley scattering. We derive Hooge's law, and the Hooge parameters for the above-mentioned processes are obtai...

Quantum 1/f noise associated with ionized impurity scattering and electron-phonon scattering in condensed matter

Theoretical calculations of electron mobility in the indirect crystals Ge, Si, and GaP are presented. The model assumes parabolic and spherical conduction band minima and includes piezoelectric, acoustic, polar, Coulomb, and intervalley scattering with appropriate electron-phonon selection rules in all cases. Fermi statistics are accounted for and no further approximations (e.g. relaxation, trial function) are made, since drift mobility is calculated from an exact iterated solution. Recent selection rules for Si and GaP lead to agreement with experiment and suggest that low-energy LA phonons are unimportant for intervalley scattering.

Electron Mobility in Ge, Si, and GaP

Electron–Phonon Interaction in n‐Si

The ohmic mobility of electrons affected only by lattice scattering has been investigated theoretically in Si. Using a displaced Maxwell-Boltzmann distribution function and considering the permitted electron-phonon interactions experimental data have been fitted to the results obtained. The results support the importance of intervalley scattering by low-energy LA phonons in agreement with Dumke, with Onton, and with previous results of the authors on non-ohmic mobility, and in disagreement with Long.

M. Costato

Papers

Lattice-Scattering Ohmic Mobility of Electrons in Silicon