Thermal Desorption of Helium Films: Theory and Experiment

The desorption kinetics of helium films is explored in the context of a phenomenological model wherein the film is assumed to have the thermodynamic properties of bulk liquid and the vapor is described by simple kinetic theory. When supplemented by the condition that desorption proceed at the maximum rate permitted by detailed balance, equations for energy and mass conservation completely determine the dynamics of the system. The model is applied to the specific problem of characterizing the time response of an adsorbed film when the equilibrium between it and the ambient vapor is perturbed by a sudden change in substrate temperature and the system subsequently evolves toward a new steady state. Analysis reveals that for infinitesimal perturbations from equilibrium the equations of motion are linear and result in exponential solutions for the time dependence of the desorption flux. For finite temperature elevations and realistic adsorption isotherms, however, the equations of motion are highly nonlinear. In either case, isothermal desorption at the temperature of the substrate is shown to be a general feature of the solutions under usual experimental conditions and this considerably simplifies interpretation of the nonlinear problem. Under these circumstances one can identify a continuous succession of coverage-dependent relaxation time scales which are given in terms of instantaneous properties of the adsorption system. These time scales are distinct from, and in general unrelated to, the coverage-dependent mean lifetime of an atom on the surface. To characterize the overall time scale of the nonlinear evolution towards steady state, a global measure is defined in terms of both instantaneous and steady-state properties and used to summarize experimental data. A direct method for measuring the relaxation time of monolayer helium films flash desorbed from evaporated metal-film substrates is described and used to test the model. The technique is based on a rapid heating scheme made possible by the unique properties of ballistic phonon propagation in single crystals at low temperature. Global time constants extracted from the data in the near-equilibrium regime agree well with the predictions of the model. When these results are combined with earlier data at higher substrate temperatures and different ambient conditions, the picture is consistent with scaling properties implied by the theory. It is shown how the particular dependence on initial conditions of the exponent in a Frenkel-Arrhenius parameterization of the global time constant may be traced to the curvature of the equilibrium adsorption isotherm. This curvature is substantiated by the behavior of the instantaneous relaxation time scales, the time-of-flight spectrum of the desorbing flux, and the kinetics of readsorption.