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

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 Γ₆ and Γ₅ levels in zero field) for the particular pairs selected. In this way, values of A between 0.5 and 50 {μ} 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 A₀exp(-2{ρ}/aD) and W₀exp(-2{ρ}/aD), respectively, for large values of {ρ}, where aD is the donor Bohr radius and {ρ} is an effective intrapair separation defined by {ρ}=r[sin²{θ}+(ε_⊥/ε_∥)cos²{θ}]1/2, where {θ} is the angle between the pair axis and the crystal c axis. Values of A were measured over the range {ρ}=1.5aD to 4aD, and values of W for the range {ρ}=4aD to 9aD.The data for A at {ρ}>2aD and for W can be fitted by the exponential laws given above, with a common value of aD=2.75 nm. The parameter A₀{}0.85 meV, and W₀{~}2×{}10⁸ s^-1. The value for aD is in good agreement with the estimate of 2.39 nm obtained from effective-mass theory. From 2aD to 9aD, 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 {ρ}2aD, the exchange splitting ceases to follow a simple exponential dependence and, as expected, tends towards the value AX=0.21 meV of the exchange splitting for the free exciton. However, the departure from the exponential law occurs at values of {ρ} greater than predicted, indicating the need for improved theories of the electron-hole exchange interaction in semiconductors.