Nonlinear parameter estimation technique for kinetic analysis of thermal desorption data

Abstract

We introduce the use of statistical methods to the analysis of thermal desorption data. With this approach, any arbitrary model (mechanism) for desorption may be evaluated by fitting each model directly to the untransformed data for the flux and temperature versus time from thermal desorption experiments. Advantages of the nonlinear parameter estimation method over other methods requiring transformation of the pressure/temperature versus time data include: (i) straightforward quantitative comparison of arbitrary competing models, (ii) the ability to estimate nuisance parameters in the model that must be assumed or known in other methods, (iii) the estimates obtained have minimum bias, (iv) meaningful error estimates may be readily obtained, and (v) information about parameter interactions obtained from the shape of the joint confidence region can show that more data are needed. Simulated data are used to demonstrate some capabilities of the approach, and temperature-programmed desorption data for diethylsilane- and hydrogen-exposed Si(100) surfaces are analyzed. Good agreement is found between the estimates presented here for the doubly-occupied dimer model for monohydride desorption from hydrogen-covered Si(100) (56 kcal mol −1 < E a < 58.5 kcal mol −1, 3 × 10 14s −1 < A < 2 × 10 15s −1, 4.8 kcal mol −1 < ΔH pair < 6.5 kcal mol −1) and the preponderance of estimates presented elsewhere, but a significant departure from these kinetics is observed for the diethylsilane-exposed Si(100) that remains unexplained.