Optical approaches to the determination of composition of semiconductor alloys during epitaxy

Realization of sample-driven closed-loop feedback control of the epitaxial growth of semiconductor alloys requires that the fluctuations of the composition of the most recently deposited material be determined over an outermost region that is ideally no more than several angstroms thick. This information is encoded in the dielectric function ε/ ₀ of the region. The standard approach for obtaining ε ₀ is to mathematically subdivide the sample into thin layers and analyze them sequentially outward from the substrate by solving the Fresnel equations. However, the feed-forward nature of this approach leads to instabilities if thicknesses are reduced below a few tens of angstroms, a value too large for practical control applications. Derivative methods avoid these instabilities by allowing ε₀ to be determined for dynamic processes involving deposition or etching even if nothing is known about the underlying sample structure. The limited accuracy of earlier derivative approaches based on the exponential-spiral form of interference expressions for optically thick films has been improved to acceptable levels with the recently developed virtual-interface (V-I) approach. Here, a background of the field is provided, the various methods of obtaining ε₀ from the perspective of control applications are discussed, and V-I theory is used to obtain analytic expressions describing the accuracy of the earlier derivative methods. For ellipsometric measurements the best combination of speed and accuracy is obtained with the virtual-substrate approximation. For situations where higher accuracy is needed, a hybrid V-I-Fresnel method is proposed that retains the stability of derivative approaches yet is exact