Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data

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 /spl epsiv///sub 0/ of the region. The standard approach for obtaining /spl epsiv//sub 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 /spl epsiv//sub 0/ 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 /spl epsiv//sub 0/ 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.

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

We show that a certain type of artificial neural systems or neural networks, more specifically the backpropagation network (BPN), can be an efficient tool in fast, approximate pre‐evaluation of spectroscopic ellipsometric (SE) measurements. The BPN is a multilayer, feedforward network which can perform nontrivial mapping functions. We demonstrate the method on separation by implantation of oxygen (SIMOX) structure and ion implantation caused damage depth profile evaluation. The results are compared with others from independent measurements.

Backpropagation (neural) networks for fast pre‐evaluation of spectroscopic ellipsometric measurements

Numerical techniques useful in the practice of ellipsometry

Optical ellipsometry has been found to be a promising technique for monitoring process parameters, such as film composition and film thickness, of semiconductor wafers grown with molecular beam epitaxy. Whereas it is a straightforward task to calculate ellipsometry angles given the thickness of the film and the refractive indexes of the film and substrate, it is a difficult task to invert that mathematical relationship. However, the process must be inverted if the measured parameters are to be interpreted meaningfully in terms of film composition and film thickness. This paper reports on the use of neural-net computing for the inverse mapping of measured ellipsometry parameters. We used a functional-link net which is very efficient in function approximation. The advantage of using the net, however, is not only its speed, but also because some other net architecture characteristics allow us to perform the task in a holistic manner.

Dong C. Park

Papers

Development of artificial neural networks for real time, in situ ellipsometry data reduction