Optical properties of ion-implanted GaAs: The observation of finite-size effects in GaAs microcrystals
We have carried out reflectivity measurements, for photon energies from 2.0 to 5.6 eV in the electronic interband regime, for a series of unannealed ion-implanted GaAs samples which had been exposed to 45-keV Be+ ions at various fluences up to 5×1014 ions/cm2. The microstructure of the near-surface implantation-induced damage layer in these samples is known (from previous Raman work) to consist of a fine-grain mixture of amorphous GaAs and GaAs microcrystals, with the characteristic microcrystal size L of the microcrystalline component decreasing with increasing fluence (L=55 Å at 5×1014 cm-2). The optical dielectric function of each sample’s damage layer has been derived from the observed reflectivity spectrum by Lorentz-oscillator analysis. Then, by inverting the effective-medium approximation, we have extracted the dielectric function of the microcrystalline component (μ-GaAs) within the damage layer. The optical properties of μ-GaAs differ appreciably from those of the bulk crystal, the difference increasing with decreasing L. We find that the microcrystallinity-induced spectral changes are concentrated in the linewidths of the prominent interband features E1, E1+Δ1, and E2. These linewidths increase linearly and rapidly with inverse microcrystal size: Γμ=Γ0+AL-1, where Γ0 is the linewidth in the bulk crystal, Γμ is the linewidth in μ-GaAs, and A is a constant. For the E1 and E2 peaks, the experimentally determined value of A is such that the finite-size broadening (AL-1) is about 0.2 eV when L=100 Å. We propose a simple theory of the finite-size effects which, when combined with band-structure information for GaAs, semiquantitatively accounts for our observations. Small microcrystal size implies a short time for an excited carrier to reach, and be scattered by, the microcrystal boundary, thus limiting the excited-state lifetime and broadening the excited-state energy. An alternative uncertainty-principle argument is also given in terms of the confinement-induced k-space broadening of electron states.