Spatial Correlation Interpretation of Effects of As + Implantation on the Raman Spectra of GaAs
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SPATIAL CORRELATION INTERPRETATION OF EFFECTS OF As+ IMPLANTATION ON THE RAIYLAN SPECTRA OF GaAs D.E. ASPNES,* K.K. TIONG**, P.M. AMIRTHARAJ**, AND F.H. POLLAK** *AT&T Bell Laboratories, Murray Hill, NJ 07974; **Physics Department, Brooklyn College of CUNY, Brooklyn, NY 11210
ABSTRACT The red shift and asymmetric broadening of the LO phonon mode of ion-implanted GaAs are both described quantitatively by a spatial correlation model based on a damage-induced relaxation of the momentum selection rule previously used by Richter, Wang, and Ley to describe similar effects in microcrystalline Si. The success of the model for a qualitatively different disorder microstructure suggests it may be possible to evaluate average sizes of crystallographically perfect regions in semiconductors from the phonon lineshapes of their Raman spectra.
Recently, Richter, Wang, and Ley [I] showed that the red shift and broadening of the LO phonon line in the first-order Raman spectrum of microcrystalline silicon could be described in terms of the lineshape and phonon dispersion data for the perfect crystal if it is assumed that the q-selection rule is relaxed in the microcrystalline material. In this model the phonon wave function in a spherical crystallite was assumed to have the form of that of a phonon in an ideal crystal except for being attenuated by a spatial 2 factor exp(-2r2/L ) representing the finite extent of the crystallite. With this assumption the phonon wavefunctions are no longer eigenstates of the crystal momentum but become superpositions of such eigenstates with a weighting factor exp(-L2(q-qo) /8), where `o is the wavevector of the initial state. Under this condition the observed first-order lineshapes become superpositions of lineshapes representing the individual eigenstates of the unperturbed crystal, and red shifts and broadenings arise because the energies of the unperturbed eigenstates are themselves functions of q. It is clear that the idea of the finite extent of a phonon wavefunction can be extended to microstructural geometries that are not microcrystalline, such as point or line defects, or sublattice disorder in the case of ternary or quaternary semiconductor alloys [2]. However, it is not clear that the spherical correlation model [1] should be applicable in these cases. To provide some insight into this question, we have measured the first-order Raman spectra of a series of single-crystal GaAs crystals of surface orientation implanted 70 off axis with 270 keV As+ as described previously [3]. The damage distributions caused by ion implantation can be calculated from LSS theory [4]; the relevant parameters describing the damage resulting from each ion are the mean damage depth = 880A, the mean straggle =350A, and the transverse straggle = 220A. Thus, the implantation damage forms a relatively narrow, approximately conical region around the track of each As+ ion with an apex angle of about 300. At small fluences these regions locally destroy the long-range order without introducing grain boundaries or other p
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