Kinetics of Radiative Recombination at Randomly Distributed Donors and Acceptors

The kinetics of the recombination of holes trapped on acceptors with electrons trapped on donors have been treated theoretically and the results compared with the observed low-temperature fluorescent decay of GaP doped with sulphur donors and silicon acceptors. The assumptions are made that the distribution of donors and acceptors is random and that the recombination rate depends exponentially on the donor and acceptor separation. The theoretical problem can be exactly solved when either the donor or acceptor is in excess, and an approximate solution is given for the case of exact compensation. The decay of the total pair emission has been measured over many factors of 10 of intensity and time and can be satisfactorily accounted for by the theory using only two adjustable parameters. If the decay occurs from a system in which all the donors and acceptors are not initially neutral, different decay curves are obtained which can be explained by assuming that the capture cross section of a pair for a hole or electron depends approximately on the square of the internuclear pair separation. The spectra have also been measured after flash excitation, and they are found to change in shape and position as a function of time. These changes can be quantitatively explained in terms of the simple theory, provided residual broadening effects from phonon interactions and other sources are included. The effects of a magnetic field at low temperature on the decay kinetics have been predicted and observed and allow the determination of certain $g$ values. At high-impurity concentrations there are deviations from simple behavior, evidently caused by complications in the chemical doping of the crystals. Experimental evidence for pair effects in the edge emission of CdS is also briefly reported. It is likely that similar decay phenomena observed in other seniconductors and phosphors can be explained on a similar basis without invoking arbitrary trap distributions. It is only necessary to assume a random distribution of donors and acceptors throughout the crystal.