Theory Of Radiative Recombination Research Articles

Rate enhancement in the recombination ofBi80+ions with electrons

Recombination of ${\mathrm{Bi}}^{80+}$ ions with electrons at low relative energies has been investigated employing the electron cooler at the experimental storage ring of the Gesellschaft f\ur Schwerionenforschung in Darmstadt. Absolute recombination rate coefficients have been determined for relative energies ${E}_{\mathrm{rel}}$ between $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and 10 eV. Simulations of cooling-force effects were carried out to assure the validity of these energies. In the range 10 meV $\ensuremath{\lesssim}{E}_{\mathrm{rel}}\ensuremath{\lesssim}10\mathrm{eV}$ the measured rate coefficients agree well with the theory for radiative recombination (RR). Towards lower relative energies ${(E}_{\mathrm{rel}}\ensuremath{\lesssim}10\mathrm{meV})$ the measured rate coefficients increasingly exceed the prediction of the RR theory. At the lowest accessible relative energy the ratio of measured and calculated rates reaches a factor of 3.5. The enhancement is found insensitive to a variation of the electron density from $1.6\ifmmode\times\else\texttimes\fi{}{10}^{6}$ to $4.8\ifmmode\times\else\texttimes\fi{}{10}^{6}{\mathrm{cm}}^{\ensuremath{-}3}.$

Recombination of U 92 + ions with electrons

Recombination of fully stripped U92+ ions with electrons has been investigated at the Experimental Storage Ring (ESR) in Darmstadt. Absolute recombination rate coefficients have been measured for relative energies from 0 to 33 eV. For energies greater than 20 meV the experimental result is well described by the theory for radiative recombination (RR). Below 20 meV the experimental rate increasingly exceeds the RR calculation as observed previously in the recombination of light bare ions as well as of Bi83+. This low-energy rate enhancement is shown to scale as Z2.6 for bare ions, where Z is the atomic number of the ion. The U92+ recombination rate enhancement is insensitive to changes of the electron density. Variation of the magnetic guiding field strength from 80 mT to 120 mT resulted in oscillations of the recombination rate at 0 eV. The oscillations are partly attributed to changes of the transverse electron temperature accompanying the change of the magnetic guiding field strength; partly they may be caused by uncompensated small changes of the interaction angle between the two beams.

Recombination of Bare Bi83+ Ions with Electrons

Electron-ion recombination of completely stripped Bi83+ was investigated at the Experimental Storage Ring (ESR) of the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt, Germany. It was the first experiment of this kind with a bare ion heavier than argon. Absolute recombination rate coefficients have been measured for relative energies between ions and electrons from 0 up to about 125 eV. In the energy range from 15 meV to 125 eV good agreement is found between the experimental result and theory for radiative recombination (RR). However, below 15 meV the experimental rate increasingly exceeds the RR calculation and at Erel = 0 eV it is a factor of 5.2 above the expected value. A variation of the electron density by a factor of 3 had no significant influence on the recombination rate which is in agreement with other experiments. An additional variation of the magnetic guiding field of the electrons from 70 mT to 150 mT in steps of 1 mT resulted in periodic oscillations of the rate which are accompanied by considerable changes of the transverse electron temperature.

Recombination of bareBi83+ions with electrons

Electron-ion recombination of completely stripped Bi83+ was investigated at the Experimental Storage Ring (ESR) of the GSI in Darmstadt. It was the first experiment of this kind with a bare ion heavier than argon. Absolute recombination rate coefficients have been measured for relative energies between ions and electrons from 0 up to about 125 eV. In the energy range from 15 meV to 125 eV a very good agreement is found between the experimental result and theory for radiative recombination (RR). However, below 15 meV the experimental rate increasingly exceeds the RR calculation and at Erel = 0 eV it is a factor of 5.2 above the expected value. For further investigation of this enhancement phenomenon the electron density in the interaction region was set to 1.6E6/cm3, 3.2E6/cm3 and 4.7E6/cm3. This variation had no significant influence on the recombination rate. An additional variation of the magnetic guiding field of the electrons from 70 mT to 150 mT in steps of 1 mT resulted in periodic oscillations of the rate which are accompanied by considerable changes of the transverse electron temperature.

Effect of laser-induced defects on luminescence in InP crystals

Experimental data on luminescence in laser-modified InP crystals are compared with the theory of radiative recombination of heavily doped, compensated semiconductors. It is established that the band with maximum at 1.35 eV observed at 77 K is due to radiative transitions through the tails of the density of states which are formed as a result of the random distribution of defects and impurities showing up after laser treatment. The effective depth of the tails of the density of states is estimated to be equal to 67 meV.

Theory of radiative recombination from the metastable excited states of quantum dots

The radiative recombination of an exciton (electron-hole pair) confined in a semiconductor quantum dot is studied within a general model based on the effective-mass approximation. The dependence of the photoluminescence spectrum on the size of the dot and the magnetic field describe well a series of recent experimental results. In particular, a characteristic splitting of the main photoluminescence peak into a doublet or triplet is observed at the critical size and magnetic field, as a consequence of the appearance of metastable states in the exciton spectrum.

Recombination of Au 25+ with free electrons at low energies

The origin of the widely observed enhancement of rates for electron-ion recombination at very low energies is still unknown. We investigated the recombination of Au25+ with free electrons in a merged-beams experiment at the UNILAC accelerator of the GSI in Darmstadt. At Erel= 0 eV we found an enormous enhancement factor of 365 compared to the theory of radiative recombination. An increase of the electron density by a factor of 10 had not much influence on the measured rate coefficient.

Theory of radiative recombination with strong laser pulses and the formation of ultracold molecules via stimulated photo-recombination of cold atoms

A time dependent theory for radiative recombination induced by strong pulses is presented. Analytic solutions in the adiabatic limit are derived and found to be in excellent agreement with exact numerical solutions. Both the pump-before-dump “intuitive” and dump-before-pump “counter-intuitive” schemes are considered. Resonantly enhanced two-photon recombination of ultracold atoms is shown to be an efficient mechanism for the production of ultracold molecules. We have performed detailed calculations on the radiative recombination of cold Na atoms by short laser pulses. Our calculations show that, per pulse, it is possible for up to 97% of all head-on Na-Na colliding pairs to end up as v=0, J=0 translationally cold Na2 molecules. We show that these findings, translated to thermally cooled ensemble conditions, mean that the fraction of Na atoms at μKelvin which can be recombined by a pulse of 20 ns duration and 108 W/cm2 peak intensity, to form J=0 molecules is 6×10−6 per pulse. With the above parameters, a laser operating at 100 Hz can convert half of an ensemble of cold atoms to cold molecules in ∼25 min. The efficiency of the process can be increased by going to longer pulses of lower intensity, by going to lower temperatures or by increasing the density of the ensemble. In particular, the “counter-intuitive” scheme which allows for use of longer pulses of lower intensities, with no spontaneous emission losses, considerably increases the yield.

Electron cooling and recombination experiments with an adiabatically expanded electron beam

Magnetically guided electron beams with transverse temperatures reduced with respect to the cathode temperature by a factor of more than 7 were realized in the electron cooling device of the heavy-ion storage ring TSR and the effect of the reduced transverse temperature in recombination and electron cooling experiments was studied. Measured dielectronic recombination resonances at low relative energy and spectra of laser-stimulated recombination indicate that transverse electron temperatures of about 17 meV have been obtained at cathode temperatures of about 110 meV. The temperature dependence of the spontaneous electron-ion recombination rate during electron cooling was investigated and found to follow the inverse square-root law expected from the theory of radiative recombination, although the measured absolute rates are higher than predicted. A new method based on analyzing the intensity of the fluorescence light emitted during simultaneous laser and electron cooling is used to measure the longitudinal electron cooling force in a range of relative velocities extending over two orders of magnitude (10 5–10 7cm/s). The results confirm the occurrence of ‘magnetized electron cooling’ also at the reduced transverse temperature and show that, compared to earlier measurements at the high transverse temperature, the cooling force increases by about a factor of 2; a considerably larger increase by a factor of ≈5 would be expected if ‘magnetized electron cooling’ would not exist.

QUANTUM WELLS IN OPTOELECTRONICS: Laser-induced transient photoconductivity in MQW systems

In the interpretation of laser-induced transient photoconductivity a number of effects have to be taken into account. The most important of these are considered to be those associated with excitons, degeneracy, photon recycling, mobility variations and the nonuniformity of carrier injection. These effects are discussed and modifications are made, by including the boson character of the exciton and its four-fold spin degeneracy, to the theory of radiative recombination. A simple estimate of the effect of photon recycling in thin MQWs is given. The density dependence of mobility in an electron-hole plasma is argued to be small, except when higher subbands become populated or the quantum wells become full. In the latter case saturation of the photoconductivity, which can occur at low laser intensities with nonuniform injection, is expected. The importance of both the exponential decay in the degenerate regime and the observed intensity dependence of the initial amplitude is emphasised.

Theory of radiative recombination by diffusion and tunneling in amorphous Si:H

A theory for geminate electron-hole recombination in amorphous semiconductors is given, which includes the effects of both diffusion and tunneling. The exact solution of the model is obtained neglecting the Coulomb interaction, which is included later in the prescribed diffusion approximation. It is shown that any combination of diffusion and tunneling will lead to a ${t}^{\ensuremath{-}\frac{3}{2}}$ long-time behavior for the reaction rate. The model is used to carry out an analysis of the photoluminescence decay in plasma-deposited amorphous Si:H as a function of temperature. The ${t}^{\ensuremath{-}\frac{3}{2}}$ long-time decay is observed at intermediate temperatures ($T\ensuremath{\sim}150$ K), and the calculated luminescence quenching is in good agreement with experiment. The initial thermalized pair distribution function of electron-hole separations obtained from the low-temperature ($T=8$ K) luminescence data is used to determine the Onsager photogeneration efficiency at room temperature. The calculations are in good agreement with the corresponding quantum efficiency obtained from recent xerographic measurements on the same material.

Theory of radiative recombination by diffusion and tunnelling in amorphous Si:H

A theory of the temperature variation of the photoluminescence decay in plasma-deposited amorphous Si:H is presented. We use the low temperature lifetime distribution (neglecting diffusion) to obtain the radial distribution function of thermalized electron-hole pairs. Neglecting the effect of temperature on the distribution function, we use the exact solution of the diffusion equation, including tunnelling, to fit the luminescence decay data at higher temperatures. The Coulomb interaction of the electron-hole pair is treated in the prescribed diffusion approximation. We also obtain an estimate of the quantum efficiency vs. electric field at room temperature.

Beitrag zur Berechnung der strahlenden Rekombinationswahrscheinlichkeit B von eigenleitendem Silicium / Contribution to the Calculation of the Radiative Recombination Probability B in Intrinsic Silicon

Quantitative calculations of Varshni, using the theory of radiative recombination of van Roosbroeck and Shock- ley yielded a slight increase of the recombination probabi­lity B with temperture T. Measurement of Schlangenotto et al demonstrated in contrast a strong decrease of B with T. It is pointed out, that this discrepancy is only a conse­quence of using approximative ni values (intrinsic carrier concentration) by Varshni. Introduction of new, corrected data of ni yields now a remarcable agreement between calculation and measurement.

The spectrum of the planetary nebula NGC 7027 from 0.9 to 2.7 microns

The spectrum of the planetary nebula NGC 7027 is presented from 0.9 to 2.7 ..mu... Emission lines of the Brackett and Paschen series of hydrogen and of ionized helium have been detected, and the intensities are shown to be consistent with the theory of radiative recombination. Three lines of the 1-0 quadrupole spectrum of molecular hydrogen have been detected. Four lines of He I, including the 2 /sup 1/S/sup -/ 2 /sup 1/P line at 2.058 ..mu.., have been observed. It is concluded that the nebula is optically thick in the helium principal series. A tentative identification of an emission line in (P II) at 1.1898 ..mu.. has also been made. (AIP)

On the Theory of Radiative Recombination in High Magnetic Field in Semiconductors

AbstractThe effect of a high magnetic field on the recombination between the conduction band and an acceptor is examined. It is found that at magnetic field which corresponds to the “quantum limit” for the conduction band but gives no “deformation” of the acceptor states, the transition matrix element does not depend on the magnetic field. The assumptions for the magnetic field are fulfilled for the case of laser radiation in a magnetic field. It may be said that on the basis of the hydrogen‐like model, the field dependence of the threshold current must be determined by the change in the density of states.

The Lifetime of Added Carriers in InSb

The Roosbroeck-Shockley theory of radiative recombination of electrons and holes in semiconductors is extended to the case of degenerate semiconductors and applied to InSb. The experimental optical absorption curves of various n-type and p-type samples are analysed and results given for the lifetime of added carriers for this process alone as a function of the position of the Fermi level. An extrapolation indicates a decay time for a small disturbance in carrier concentration in intrinsic material of 0.75μsec. Comparison with experimental results indicates that this process may be predominant in InSb.