Electron-hole exchange interaction for donor-acceptor pairs in CdS determined as a function of separation distance by optically detected magnetic resonance.

Abstract

This paper describes the first investigation of the way in which the electron-hole exchange interaction for a donor-acceptor pair depends on the separation r between the donor and the acceptor. The case studied is that of shallow donor electrons interacting with shallow acceptor holes in CdS. The electron-hole recombination produces the well-known green edge emission, which is studied here by optically detected magnetic resonance (ODMR) and by time-resolved (TR) luminescence spectroscopy.Coulomb shifts cause the energy of the zero-phonon photoluminescence transition to depend on r, so that pairs of a given separation can be studied selectively by appropriate choice of the observation wave length. The exchange interaction produces line splittings in the ODMR spectra, which give a direct determination of the exchange constant A (the separation between the ${\ensuremath{\Gamma}}_{6}$ and ${\ensuremath{\Gamma}}_{5}$ levels in zero field) for the particular pairs selected. In this way, values of A between 0.5 and 50 \ensuremath{\mu} eV can be measured.The TR luminescence experiments were conducted in order to establish the relation between observation wave length and the value of r; they also provided measurements of the radiative recombination rate constant W. The parameters A and W are expected to have the form ${A}_{0}$exp(-2\ensuremath{\rho}/${a}_{D}$) and ${W}_{0}$exp(-2\ensuremath{\rho}/${a}_{D}$), respectively, for large values of \ensuremath{\rho}, where ${a}_{D}$ is the donor Bohr radius and \ensuremath{\rho} is an effective intrapair separation defined by \ensuremath{\rho}=r[${\mathrm{sin}}^{2}$\ensuremath{\theta}+(${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$/${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\parallel}}}$)${\mathrm{cos}}^{2}$\ensuremath{\theta}${]}^{1/2}$, where \ensuremath{\theta} is the angle between the pair axis and the crystal c axis. Values of A were measured over the range \ensuremath{\rho}=1.5${a}_{D}$ to 4${a}_{D}$, and values of W for the range \ensuremath{\rho}=4${a}_{D}$ to 9${a}_{D}$.The data for A at \ensuremath{\rho}>2${a}_{D}$ and for W can be fitted by the exponential laws given above, with a common value of ${a}_{D}$=2.75 nm. The parameter ${A}_{0}$\ensuremath{\simeq}0.85 meV, and ${W}_{0}$\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. The value for ${a}_{D}$ is in good agreement with the estimate of 2.39 nm obtained from effective-mass theory. From 2${a}_{D}$ to 9${a}_{D}$, the values of A and W change by 6 orders of magnitude and the results provide one of the best demonstrations ever obtained that the tail of a donor envelope function can be described by a single exponential out to very large distances.For \ensuremath{\rho}2${a}_{D}$, the exchange splitting ceases to follow a simple exponential dependence and, as expected, tends towards the value ${A}_{X}$=0.21 meV of the exchange splitting for the free exciton. However, the departure from the exponential law occurs at values of \ensuremath{\rho} greater than predicted, indicating the need for improved theories of the electron-hole exchange interaction in semiconductors.