Estimating pre-exponential factors for desorption from semiconductors: Consequences for a priori process modeling

Quantitative estimation of gas desorption rates from semiconductor surfaces is playing an increasingly important role in designing and optimizing device manufacturing processes. Typical rate expressions use a simple Arrhenius form for the rate constant with an activation energy E _d and pre-exponential factor ν. In the absence of experimental data, E _d can often be estimated via standard quantum methods. This approach does not provide an estimate of ν, however, so modelers often simply set ν equal to a typical vibrational frequency near 10 ¹³ s ^-1 . The present work surveys the available experimental literature to assess the likely validity of this procedure. We show that, like metals, semiconductors commonly give prefactors differing from 10 ¹³ s ^-1 by many orders of magnitude. A brief survey of theoretical treatments of desorption shows that numerous factors can account for this variability, although the factors operating in any specific case cannot usually be identified ahead of time. The resulting uncertainties in estimating ν significantly reduce the reliability of a priori process modeling for operations involving gas-solid reactions, and the results of such modeling should be viewed with proportionate circumspection.