CHARACTERIZATION OF InGaAsP SUPERLATTICE SYSTEMS USING ROCKING CURVE SIMULATIONS

Abstract

Semiconductor superlattices and quantum-well heterostructures form an important class of electronic and optoelectronic materials since the properties of these layered structures are in many ways superior to those of bulk materials. While most superlattices and quantum-well heterostructures are grown using lattice-matched materials, structures composed of lattice-matched heterolayers are also of considerable interest since the loosening of the lattice-matching constraint allows increased flexibility in choosing constituent materials. Although strained-layer superlattices (SLS) were first studied in the early 1970's, a significant fraction of strained-layer work has occurred in the past years. Comprehensive reviews of strained-layer structures in several different semiconductor material systems are available. Progress in the fabrication of pseudomorphic semiconductor structures has led to the development of photoexcited lasers, quantun-wcll injection lasers, light-emitting diodes, photodetcctors and high electron mobility transistors, which utilize strained layers. Although electronic and optoelectronic devices often utilize SLS quantum-well heterostructures, studies of pseudomorphic material properties tend to emphasize on superlattice structures composed of multiple interacting strained layers. In properly designed strained-layer structures, the mismatched layer is so thin that the difference in lattice constants of the constituent materials is accommodated by elastic strain rather than by the generation of misfit dislocations. Thus, strained-layer structures of high crystalline quality can be fabricated from semiconductors differing signi ficantly in their bulk lattice constants, provided layer thicknesses do not exceed strain-dependent critical values. Variety of expitaxial growth methods like LPE, VPE, MOCVD, MBE are available for fabrication of high quality structures. \\ Characterization of grown SLS is possible with optical and electrical measurements, transmission electron microscopy, and double crystal X-ray diffrac tion, etc. Double crystal X-ray diffraction is a nondestructive method. The rocking curves obtained experimentally can not give all the necessary and required structural details of the individual layers. If the SLS structures undergoes any thermal treatment, diffusion of impurity, ion-implantation etc., then a knowledge of the effects of such processes near the interface is important. Also these processes cause disordering of the SLS structures due to intermixing. The use of X-ray double crystal diffraction technique in characterizing multilayer structure by means of experimental rocking curves is,however, compli cated since the rocking curves in general are of complex nature in which there is no longer one-to-one correlation between diffraction peaks and individual layers in the structure. This problem is overcome by using dynamical scattering theory to generate simulated rocking curves based on an assumed material structure. The theoretical and experimental rocking curves are then matched by an iterative process whereby the assumed distribution of strain in the layers is modified until a good fit is obtained with the. experimental data. A careful study of existing literature shows that kinematical theory as well as dynamical theory of X-ray diffraction are two well known models based on which rocking curves can be simulated. The kinematical theory model has been used by a number of workers in view of its simplicity, while very few have worked with dynamical theory and no dynamical treatment have been used for the study of impurity diffused or ionimplanted SLS. The kinematical theory* however, is not applicable to heteroepitaxial layer or implanted layers with thicknesses that are a significant fraction of the extinction distance. The kine matical theory ignores extinction effects. When the reflecting power is more than about 6% the kinematical theory is not suitable. m Keeping in view all these points in the present studies,a dynamical theory has been preferred. Two dynamical models are presented. One is based on Takagi- Taupin's derivation and the other one based on Abeles' matrix method. In the simulation, a one dimensional strain variation is assumed normal to the sample surface i.e. the epilayers are elastically strained under a tetragonal distortion and are lattice-matched in the plane of the sample surface. For this type of unidirectional strain variation the well known Takagi-Taupin equations have been simplified and solved for epilayers of SLS structure, to give the ratio of the diffracted to incident beam amplitudes. For the calculation of layer reflectivity the epilayers in the SLS structure is divided into thin uniform laminae each of constant lattice-parameter and the reflectivity calculated by starting at the substrate and working upwards through each layer to the top layer. Finally rocking curves were convoluted with the reference crystal rocking curve. Some illustrative examples of simulated rocking curves using different combinations of composition, thickness, and number of periods of SLS structures have been shown. Further rocking curves of a number of SLS experimental specimens namely InGaAs/GaAs, InGaAs/InP, and GaAsP/GaP reported in the literature have been simulated and a comparis on is made. Initial data from experimental rocking curves were used to calculate rocking curves for SLS structure. The input data are slightly adjusted about their initial values until a reasonable fit with experimental curve is achieved. For the initial data a know ledge of thickness, number of periods, mismatch variation of layers within each period is required. These can be obtained from SLS growth conditions. From such a comparis on an accurate assessment of composition, mismatch, thickness of period and number of molecular layers have been achieved. The simulation technique has also been successfully applied to characterize thermally annealed and Zn diffused disordered InGaAs/GaAs SLS. For thermally

annealed super-lattices the composition in the real space, assuming a simple linear diffusion mechanism in a single well has been considered while for Zn diffused disordered superJattice the interstitial and substitutional mechanism has been used to calculate the composition profiles. Further, modification of this technique have been used to assess the strain/ damage depth distribution in an ionimplanted SLS structure. In this approach the strained-material is modeled as a series of laminea each with a perpendicular strain and damage assumed uniform. Damage is assumed as a random displace ment of atoms from their lattice sites. This was taken to have the form of a spherically symmetric Gaussian function with standard deviation U. The lattice damage and additional strain in Beryllium implanted GaAsP/GaP SLS structure have been assessed by comparison of an experimental with simulated rocking curve. In the Abeles' matrix method a 2x2 matrix is described to compute reflection and transmission of light by plane layered media in which the refractive index is isotropic and varies only in the direction normal to the layers. The method can be used to find solutions for dynamical theory of X-ray diffraction if variation of X-ray refractive index normal to any sets of Bragg planes of interest is known. In the present thesis Abeles' dynamic approach has been successfully applied to simulate rocking curves for the SLS structures. Rocking curves simulated for different composition, thickness of epilayers, and number of periods of SLS' structures have been studied extensively and compared with those simulated by Takagi-Taupin's model. Comparison showed that the Abeles' approach need less computation time and gives more sharp peaks. The approaches of Takagi-Taupin and Abeles' were both used to simulate rocking curves for an experimental InGaAs/GaAs SLS structure. The satellite peak intensities thus calculated were compared with those calculated from kinematical approach and experimental data. A three crystal X-ray scan of InGaAs/InP superlattice structure reported in the literature have also been simulated using the Abeles- Takagi approach and a comparison is made with kinematical step model. On the basis of the comparison final conclusions are made.