Publisher Summary This chapter is concerned with spin-resonance absorption—that is, power absorption from an oscillating magnetic field—by conduction electrons. The e place of spin resonance in investigations of the band structure contrasts the cases of paramagnetic salts and conductors. In the former, the levels of the ions are discrete; when they have an odd number of electrons each level is at least twofold degenerate. An external magnetic field splits this degeneracy. The microwave spectroscopy of the energy bands is not confined to spin resonance, but includes cyclotron resonance. Of the two, undoubtedly the latter provides the most direct information on the energy bands. Spin resonance does not play the central role that it does in paramagnetic salts. However, it usually plays a useful supplementary role when something about the band structure is known, serving either as a check on the band model or determining the values of additional parameters. The use of spin resonance in semiconductors and semimetals grow as better materials are made and detailed knowledge about their band structure becomes available.

g Factors and Spin-Lattice Relaxation of Conduction Electrons

Improved experimental data have been obtained between 20° and 350°K for the widths and temperature shifts of the R lines in ruby. Above 77°K the results can be accurately described in terms of Raman scattering of Debye‐model phonons. There is no evidence for measurable contributions to the widths and shifts from direct processes involving emission or absorption of a single resonant phonon. Below 77°K the principal contributions are from crystal inhomogeneities.

Linewidth and Temperature Shift of the R Lines in Ruby

Under suitable circumstances imperfections in semiconductors can bind electrons (holes) with a binding energy small compared to the intrinsic energy gap of the host; the wavefunctions characterising the energy levels of the imperfection are extended over many lattice spacings. This review discusses the electronic energy levels of chemical impurities in the classic group IV elemental and the III-V and II-VI compound semiconductors. The large dielectric constant of the host, the anisotropic effective mass tensor and/or the small effective mass of the charge carrier are the factors which play a significant role in the description of the electronic energy levels; they can be viewed as scaled-down versions of the hydrogen atom with bound states having binding energies orders of magnitude smaller than those of the hydrogen atom. The authors present the experimental results on the spectroscopy of donors and acceptors in semiconductors together with the theory necessary for their interpretation. They discuss the experimental results and the theory of the bound states of impurities in the context of the symmetry and the effective-mass parameters of the band extrema with which they are associated. Effects of external perturbation-piezo- and magneto-spectroscopy-are presented both from experimental and theoretical points of view. The review concludes with the experimental observations on the linewidths of the excitation spectra of donors and acceptors in semiconductors and an analysis of the causes underlying them.

https://iopscience.iop.org/article/10.1088/0034-4885/44/12/002/pdf

Spectroscopy of the solid-state analogues of the hydrogen atom: donors and acceptors in semiconductors

Publisher Summary The Jahn–Teller effect is the intrinsic instability of an electronically degenerate complex against distortions that remove the degeneracy. Until recently, most of the effort in this field has been theoretical, and there has been more emphasis on mathematical sophistication than on the prediction of observable effects. In the past year or so, this situation has changed. Theoretical predictions have been made that can be tested rather directly against experiment. This chapter presents a general account of the basic theory and its possible applications. It applies this theory to the particular problem of a doubly degenerate electronic state interacting with a doubly degenerate vibrational mode. It extends the treatment to triply degenerate states and deals with the problem of electronic transitions involving degenerate states. In each section, as the theory is worked out and applied to particular cases, experimental results are quoted to illustrate how well (or how badly) the theory works out in practice. By this means, this chapter attempts to draw attention to gaps both in the experimental data and in theoretical understanding.

The Jahn-Teller Effect in Solids*

An extensive calculation of the optical-phonon-assisted transition rates for non-adiabatic electronic hopping motion in a solid is presented. Holstein's Molecular Crystal Model is used as a basis for study and the computation involves no restrictions on either the magnitude of the electron-lattice coupling strength, the temperature, or the difference between the electronic energies of the initial and final sites. In the strong-coupling small-polaron regime, the jump rates, associated d.c. conductivity, a.c. conductivity, and electric-field dependence of the d.c. conductivity, for a crystal are all calculated. These transport properties manifest qualitatively distinct behaviours corresponding to whether the temperature is above or well below the optical-phonon temperature. In the low-temperature regime the energy-conserving processes which involve the absorption of the minimum amount of vibrational energy provide the dominant contribution to the thermally activated jump rates. At sufficiently high...

Phonon-assisted transition rates I. Optical-phonon-assisted hopping in solids

The theory of line broadening given by Lax is found not to apply to shallow impurities in Ge and Si. Observed broadening may be instrumental at low temperatures and may be due to lifetime broadening through phonon interaction at nitrogen temperature. Calculations suggest that $p$-type spin resonance in germanium and silicon may be observable.

E. O. Kane

Papers

Phonon Broadening of Impurity Lines