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 A{} 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: Γ_μ=Γ₀+AL^-1, where Γ₀ is the linewidth in the bulk crystal, Γ_μ 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 A{}. 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.