It is shown that already at fairly low electronic densities (of the order 1014 cm-3) an electron exchanges energy with other electrons quicker than with lattice vibrations, mainly because collisions with the latter are nearly elastic. The notation of an electronic temperature T, which in an external field is higher than the lattice temperature, is then introduced and it is shown that a stationary state becomes impossible if the field is above a critical strength Fc the breakdown strength. For nonpolar and for polar substances Fc can be expressed in terms of the electronic mobility in weak fields, and of other measurable quantities.

https://iopscience.iop.org/article/10.1088/0370-1301/69/1/304/pdf

Dielectric Breakdown in Solids

The variation of the electron mobility with an increasing applied field and also the collective dielectric breakdown field, are calculated assuming that interelectronic collisions are sufficiently frequent to determine the energy and momentum distributions of the electron gas. At high temperatures a small increase (by a factor less than 2) and at low temperatures a large decrease (by a factor greater than 10) in the mobility should be observed as the field approaches the breakdown value. It is also shown that the mobility variation at high temperatures will be substantially the same if interelectronic collisions are not predominant, but at low temperatures there will be no variation at all. The application of these results to semi-conductors where the electron scattering mechanism is uncertain is discussed with special reference to indium antimonide.

The influence of interelectronic collisions on conduction and breakdown in polar crystals

Reviews the vibronic properties of point defects (i.e. impurities and radiation-induced defects) in diamond. Cases discussed are: defects where the totally symmetric electron-lattice interaction dominates; cases of dynamic Jahn-Teller distortions; vibronic interactions between nearly degenerate states and a statically deformed defect. Before discussing each of these topics the relevant theory is outlined at an introductory level with the emphasis on features relevant to understanding data. It is shown that a good understanding of the vibronic data is now available in diamond. Compared to defects in silicon, defects in diamond are less prone to static deformations, partly as a result of the high-energy transverse acoustic modes in diamond.

https://iopscience.iop.org/article/10.1088/0034-4885/44/7/003/pdf

The Jahn-Teller effect and vibronic coupling at deep levels in diamond

The potential of certain color centers to make efficient broadly tunable cw lasers for the infrared is discussed We show how the range 09 ≲λ≲33 μm can be covered by using FA(II), FB(II) and F+2 centers The pertinent physics of these centers is reviewed and appropriate laser cavity configurations are discussed The construction and performance of an advanced FA(II) laser is reported Finally, the possible use of color centers in distributed feedback devices is discussed

Broadly tunable lasers using color centers

Switching and breakdown in films

The \(\varGamma^{-}_{4}\)-mode phonon interaction in the relaxed excited state (RES) of the F center has been investigated through a theoretical study of the Stark effects on the RES, as an extension of the Kayanuma and Toyozawa theory. The general expressions of the temperature dependence of both the Stark polarization P ( T ) and the radiative life time τ( T ) are derived. They include two parameters; 2 s -2 p electronic energy difference Δ , and \(\varGamma^{-}_{4}\)-phonon coupling constant S 1 . These parameters are determined by theoretical curve-fitting of the experimental data of P ( T ) for potassium and rubidium halides. They give a consistent explanation of τ( T ) for KF, KCl, KBr, and RbCl, and also give the values of the other important parameters of the RES. It is concluded that, in the RES, Δ ≥0; this implies that the 2 s state lies either below the 2 p states or degenerates with them before introducing the electron-phonon coupling.

Vibronic Theory of the Stark Effects on the Relaxed Excited State of the F Center

The secondary emission RSE emitted after resonant excitation of F center in KCl has been measured over the whole Stokes range at 80 K. The degree of polarization P defined for the RSE intensities parallel and perpendicular to resonant light polarization is measured over the same range. The spectrum of P is divided into three successive regions; the depolarization range at the one-phonon Raman scattering, the near plateau range, and the depolarization range down to vanishing. The former two are found to depend on the resonant photon energy. The latter may be caused by the level crossing of 2 s - and 2 p -like electronic states during non-radiative process.

The Resonant Secondary Emission of the F Center in KCl at 80 K

The vibronic scheme of the relaxed excited state (RES) of the F center which includes the \(2 \varGamma_{1}^{+}\), \(\varGamma_{3}^{+}\), and \(\varGamma_{4}^{-}\)-mode interactions has been developed. Formulae of the morphic effects have been derived. The vibronic parameter values for NaF, KF, KCl, KBr, RbF, RbCl, and RbBr are determined from the consistent analysis of the temperature dependence of the radiative lifetime and of the Stark polarization. Available data of the temperature dependence of the stress-induced polarization are consistently explained. Using parameter values, the dipole moment and stress coupling coefficient (\(\varGamma_{3}^{+}\)-mode) are determined; the red Stark shift is interpreted. By including the spin-orbit interaction, the forms of the magnetic effects are derived. The spin-orbit interaction constant, the orbital g -factor, and the spin polarization in the RES are determined from the analysis of experimental data.

Vibronic Scheme of the Relaxed Excited State of the F Center

Magnetic circular polarization (MCP) of F centar emission has been measured for KCl, KBr, KI, RbCl, and RbBr. The optical pumping cycle is proposed to include three spin mixing parameters in absoption, radiationless decay ( e r1 ), and emission processes. From the analysis of experimental data using formulae derived from rate equations for the cycle, para- and dia-magnetic components ( Δ p and Δ d ) of MCP, and the spin mixing parameters are determined. Pumping photon energy dependence of Δ p are observed. It shows that e r1 for KBr depends on photon energy and predominates the net spin mixing parameter ( e t ). Temperature dependence of Δ d are shown to be relevant to the spin orbit interaction in the relaxed excited state of F center. The source of the discrepancy found between our determined values of e t and those by other schools is clarified.

Magnetic Circular Polarization of F Center Emission and the Spin Mixing Processes in Optical Cycle

The Stark effects in F center emission have been investigated for KBr, KI, RbBr, and RbI crystals as a function of emission wave-length and polarization, electric field amplitude, and sample temperature, with using a PbS IR detector. Observed results are qualitatively similar to those measured by Bogan and Fitchen for several other alkali halides. The Stark polarization and the first moment change (a red shift) of the emission band are quadratic in electric field strength; their coefficients are tabulated. Two different theoretical forms of the temperature dependence of the Stark polarization P ( T ), which have been derived by Bogan and Fitchen, and Ham and Grevsmuhl, respectively, are found to be invalid to explain the experimental data consistently. A phenomenological form to describe P ( T ) is proposed by introducing a new parameter.

Hiroshi Ohkura

Papers

Vibronic Theory of the Stark Effects on the Relaxed Excited State of the F Center

The Resonant Secondary Emission of the F Center in KCl at 80 K

Vibronic Scheme of the Relaxed Excited State of the F Center

Magnetic Circular Polarization of F Center Emission and the Spin Mixing Processes in Optical Cycle

Stark Effects in F Center Emission in KBr, KI, RbBr, and RbI Crystals