Remarks on the Recombination of Electrons and Donors in n‐Type Germanium

Abstract

The cascade theory of the recombination of electrons into ionized donors is critically examined in this paper. It is shown that in Lax's model, and also in the work of Hamann and McWhorter, the neglect of lower lying states leads to an overestimate of overestimate of the sticking probability. It is also shown, that the model proposed by Ascarelli and Rodriguez ‐ which neglects the higher excited states ‐ does not lead to the experimental value for the total capture cross‐section.

Time-Resolved Dynamics of Shallow Acceptor Transitions in Silicon

“…For a simple two-level exponential population decay with decay constant T 1 , the Fourier transform produces a Lorentzian line with full width at half maximum of 2Á FWHM ¼ 1=T 1 . Natural silicon samples exhibit strong inhomogeneous broadening due to impurities, defects, alloying, and strain so that their linewidths are much greater than this intrinsic minimum [12,26,28], though isotopically pure silicon has been shown to produce much sharper lines [16,17,20] that are close to ideal. The linewidths from the absorption spectrum (FTIR) of isotopically pure material [17] for Si:P and Si:B, and inverse lifetimes from the pump-probe experiments (this work and Ref.…”

“…Following [26], an approximate expression for the acoustical phonon emission rate via the deformation potential, at zero temperature, is…”

Far-infrared spectroscopy of bound and free electrons in III-V and II-VI semiconductors. I. Transitions between excited states observed in Zeeman spectroscopy of the shallow donor impurities

“…The probability of ionization by phonon absorption is a strong function of temperature and of angular momentum of the state concerned. Because of the presence of many intermediate states lying below the conduction band edge, the probabliity of thermal ionization has an apparent activation energy much less than the ionization energy AEi (energy separation between the conduction band and the state of interest) as has been shown by the calculations of Beleznay and Pataki (1966) and by the experiments of Stillman et al (1972). Beleznay and Pataki (1966) have shown that neglect of the intermediate states can easily lead to errors of five orders of magnitude in the estimation of sticking probability P (= 1 -I where I is the probability of ionization).…”

“…Thus the temperatures at which the photothermal mechanism operates are just those at which the excited states of the impurity have the thermal population necessary for the appearance of the excited state structure presently reported. The different probabilities of thermal excitation into the conduction band at zero magnetic field have been calculated for various states and a number of temperatures (Beleznay and Pataki 1966). In any comparison of the intensity of the exctited-state lines with those originating from the ground state the details of the thermal ionization process must be considered in addition to the equilibrium populations of the states concerned together with the matrix elements and widths of the photon-induced transitions.…”

First-principle calculation of the recombination cross-section assisted by acoustic phonons at shallow impurities in semiconductors

“…Within Lax's approach [1] one has to resort to the sticking function. This function accounts at a kinetic level for the probability a carrier has to finally reach the ground state of the impurity without returning to the conducting band, and its determination remains a complicated affair [6][7][8][9][10]. As a result, the effect of excited impurity levels during recombination remains hidden in spite of its recognized importance in determining the dynamics of recombination [ll] and low-temperature breakdown phenomena [12].…”